I'll try to touch on a few points just to try and give a "broader" perspective.
My daughter's father is a good "part-time" parent who makes his own schedule. If he doesn't want to show up, he won't. If being a parent is a hassle at the time, he will step away from that role. And then pop back in and pretend to be super dad for a brief moment to make up for it. My daughter has an unrealistic view of him. That he is as much supportive and loving as I am only because of his brief super dad moments.
You've said it yourself- he's a good "part-time" parent. Now I can't say for sure what he does or doesn't do, however from what you've said, if he is a good Father when he's there- it's unfair to belittle it with "pretend" and "super-dad" terms. If he's doing it repeatedly, making an effort- that's a good thing.
Nobody is perfect by any means, regardless of his freqency of visits or length and his personal life issues- he's making an attempt. He may not be on the perfect track of life, but he makes an effort to see his daughter- this is no bad thing.
I want her to make her own decision about him so I don't badmouth him and I don't tell him he can't be around even if months have passed since she last saw him.
She's 4 years old. 4. You cannot expect a 4 year old to "make a decision about him". You also should not be badmouthing him- regardless of what your feelings are as the fact is- he's her Father and she enjoys the time with him. Unless he's putting bad habits on her and is doing anything directly damaging towards your daughter, he's still making an effort.
Badmouthing the other parent to your children is one of the worst things you can possibly do- she's far, far to young to understand or be able to correctly form decisions on such things. Even if she's older, it's not fair on kids to say these things- I don't have a great relationship with my Mother for some very justified reasons, but my Father still wouldn't want to hear me badmouthing her regardless.
He randomly calls and they exchange "I love you"s that bring me to tears. But then when I'm on the phone he wants to discuss giving up his right and not being in her life at all. He can't decide between if she is better without him than him being part time and he refuses to be a full time committed father.
This is adorable- but bear in mind that this doesn't sound like a clear-cut case of him saying he can't be bothered- he recognises, perhaps, that he's not the best influence on her with being in prison frequently and that his time with her is sporadic and unpredictable: he knows this is a negative thing against him in terms of his daughter and perhaps is more worried about how this can effect her.
It's not, also, a matter of being a "full time committed father"- clearly you've split and you're getting married- he'll only ever be a part-time parent. I'd be glad he makes an effort, sure it isn't ideal but it's better than him not being around at all. Don't get me wrong- I can see your frustrations, but under the circumstances, he's doing a much better job than many by making an effort at all.
Her past four years of life he has gone to jail 5 times. He paid child support maybe two times. And in between his trips to county he maybe sees her a couple of weekends and then goes months without seeing her and goes back to jail.
Would it be accurate to say since birth, then?
Under the view that he's been in jail, it's arguable that expecting him to pay child support is presumably rather difficult? I'm not intimately familiar with the US justice system or laws in this regard so do forgive me- but if he's in and out for extended periods and assuming that for someone with his record finds it hard to get a stable job, this is possibly an unrealistic expectation.
She is very smart. She knows he is in jail again. He has two more years. She doesn't want to go to the jail and I don't blame her. She wants dad to get better and come see her.
She sounds like a wonderful, clever little girl- however I would say that if his latest term is to be in there for two years? That's a long, long time for them to not see each other. From the sounds of things you almost seem to be encouraging or supporting her not seeing him, which is a shame, sad and unfair on his part as if he'd like to see her, there's no harm in trying to encourage her to make an effort. If it's clearly not working out, then fair enough- but two years? You can't hang a 4-year olds not wanting to do something on him and her missing out on 2 whole years of seeing each other.
But the reality is: He isn't ever going to be a full time committed dad, he doesn't want to be.
I don't know how to tell her that. And he keeps building up her hopes that someday it will happen and she's waiting for it and she is going to be crushed when he is out of jail and it's not like he implied it would be. She asks me questions only he can answer and he refuses to be truthful with her about his intentions.
You can't say this for sure- there's no shortage of "180' turnaround" tales out there and it wouldn't be fair for you to tell your daughter this either. You can give maybes, or possibilities- but can't say for sure. You don't "need" to tell her this at all. The best you can do is to answer what you can in the best way for everyone, not just your own viewpoint.
If she asks questions only he can answer, the best person for her to speak to is him - you can't have it another way. You just plain don't know if she's asking you things only he does.
What are his intentions? Only he knows for sure and if you think you do, what are they? At best, this can be that he does want to take a frequent role in her life- he makes an effort to call and would probably like to see her in person if he can, which he doesn't have to but does. At worst, he'll peter out the visits and in time they'll stop. But you don't know this 100% for certain.
I feel responsible for encouraging a relationship when I know long term it's emotionally damaging to her.
From what you've said you've supported, not encouraged. This is all you can do as a parent in your situation. You aren't forcing her to do anything, she actively wants to speak to, see and spend time with him. If you're preventing her from doing that, that's a problem- but that isn't the case.
You can't wrap your children in cotton wool to the realities of life and the spears it throws at you- if he goes one way or the other, that's on him- it's not down to you to choose for her when she will or won't see him, or if she should continue to have contact. You will end up being the "bad guy" in her eyes for stopping any of it happening.
Support her as best you can. If he can and does visit, or wants to talk to her on the phone, let them have that. If you can support her to see him as well while he's in prison, do so. Cutting either of them off isn't just unfair it would be wrong- he's still got rights and while he's making an effort there's no harm in this.
Her father doesn't approve and is jealous that my fiancé is raising his daughter better than he is because he is in jail.
Whether this is opinion or fact isn't clear- regardless though, so what if he's jealous? He's clearly not in a similar position with a stable job, house and all the bells and whistles and some parents find it very hard to cope with the idea that another person is raising their child for the majority of the time. This isn't a bad view on your soon to be husband, it's a simple case of he knows he can't provide the same as "the other guy" can so feels inadequate about it. That's human nature.
He treats both girls the same. Her father doesn't approve and is jealous that my fiancé is raising his daughter better than he is because he is in jail.
Again is this opinion or what he's said directly?
Irrespective of the fiance, this can't be avoided if he's jealous- he's in no position to do better at current and is going to feel inadequate as a result. If you were in the same position as he, you would too- it's not nice to hear from someone else. He already has limited contact and knows that in the intervening time he's not there, someone else is providing for and receiving affection from his daughter.
And she loves her step dad and told her biological father that she calls him dad too and she likes having two dads who love her. He hates that and her having a step parent is part of the reason he is wanting to disappear after jail and not be involved at all
As above, it's difficult for a parent to hear that their child is calling someone else "dad"- this is something he has to deal with though. He either will or he won't. There's not a lot you can do about this as it's down to him to process this and come to terms with it.
Has he directly said this is why he wants to "disappear" or is this a summarized impression? As before- this is more down to his feeling of inadequacy and thinking what is best for her, though it's not an easy decision to make as it means giving up his rights and potentially contact with her.
I keep telling him how much he means to her and he needs to just step up but he refuses.
"Step up" in terms of what, exactly? There's a lot of ambiguity that goes into saying that. He obviously can't do more than be a part-time parent to her, as you're going to get married, so his involvement is solely going to be revolving around his daughter.
In that department, even if he isn't in jail how do things work for him? If he's unable to find a job and has to resort to crime to pay bills or get by, from his perspective this isn't a realistic expectation you're putting on him.
I don't know if I should be doing something else other than what I am. I comfort her when he breaks her heart but I allow him to keep coming back afterward because she is supposed to have a relationship with him. I feel like I shouldn't. I feel responsible because I let him back in after he walks out in her but I feel like if I get full custody and his parental rights are taken with it (because he will give them up if I get full custody), then she will blame me for his absence all her life and he will basically be the victim dad that got his daughter taken by the awful selfish mom. I'm trying, I really am, to do this correctly but there are so many variables and I don't know if I'm doing something terribly wrong because I feel like I am.
Don't cut off contact with him. Encourage your daughter to see him, speak to him and spend time with him. The last two seem fine (when he's not in prison) but it wouldn't hurt to try and get them face to face. It's important to them both and it's unfair to not try and give them the opportunity.
You're her mother and you have her with you all the time- so of course you'll be comforting her when things don't go right. However it's not a matter of "allowing" him to see her and spend time with her- because yes, she does need a relationship with him. Every parent has a bond with their children, however weak or strong and with them it's no different. If you were to try and stop it in any way, then yes you would be doing things wrong and be causing harm- as if there isn't a detrimental effect on her from these visits or time with him, then there's really no good reason to other than your personal feelings, rather than actual substantiated facts.
Now, if you get full custody etc this doesn't mean anything bad will happen- it doesn't mean that they won't still be able to remain in contact, the only difference is that if that becomes the case, you do have control over it. But yes, if you choose to prevent it happening, then you probably will get viewed as the bad guy in the whole situation.
The best you can do is to continue as you are and try to look on the positives- he makes an effort, he does spend time with her in whatever way he can. It isn't ideal that he's in prison, no, however under the circumstances he lives under, that you don't, you need to be realistic in your expectations of what will happen as a result. It may not be easy for him to just up and come over to see her, his own plans may fall through if he's relying on others- there isn't enough information available to fairly judge on his behalf here but regardless, he still does try and that's what matters.
She needs to have a relationship with her father- that's the bottom line. He doesn't sound like a "bad guy" overall, though obviously with going to prison there's something there, but if they enjoy seeing each other, this is irrelevant. He's not taking her out and doing bad things, giving her bad habits or leading her astray morally- she sounds like a clever nut and let's face it, as she gets older then it'll be down to her if she wants to maintain contact, not you.
Your responsibilities as a parent are entirely down to your own style, reason and rhyme at the end of the day- but I would say it's best to be fair: Although they may not get regular, frequent contact, do the best you can. Give her and him the opportunity to do what they can with each other. If in the future, circumstances change and he becomes an active "problem", that's a seperate issue, but for now? Let them have the chances they get.
Don't belittle him to her, or impose your opinions. If he's a good father when he's able to be, that's all that matters to her- she may be upset when he can't see her, or plans don't work out- but this is life at the end of the day and if there were more to work with from his side, I could say more. But as it stands, it's a sad situation but not one that you can't see the sunny side on if you try.