Let me begin by reassuring you that you are far from alone. Many kids are far better behaved for their teachers, day care workers, other family members etc. etc. They test the ones that are with them most, love them the dearest etc (they know your buttons better than anyone's after all). At five and a half, your daughter is also experiencing a big year (if in the states) starting K at 5 can be quite a change in academic expectation and exhausting on top of everything else.
Additionally, for whatever reason, it is reasonably common (at least in my experience) for mothers and daughters to rub each-other the wrong way while the father of the same daughter will make everyone that sees them, sick with envy at how well behaved the daughter is (and vice versa for mothers and sons). I think in reality, the problem is really that we have the hardest time with the kids that are most like ourselves.
So, give yourself a break and don't compare her behavior with you to her behavior with others. It isn't just you that is different, but the combination of the two of you with your own unique relationship.
Having said that: you start out by questioning how connected you are.
Make sure you haven't lost your sense of humor
Moms get chained in as the main disciplinarian quite often these days. We keep everyone (including husbands/boyfriends) on schedule, healthy, clean, the house cleaned, fed. . . and it can be easy to get too serious. However, kids need us to laugh and have fun with them too - often, the best way to win over a difficult kid is to start laughing with them again. I wrote this blarticle, How to Be the Coolest Parent in Town, a long time ago (I'm not even keeping the blog anymore) but maybe the "Silly Things" part of the article will have an inspiring idea for you.
Take a Day To Reconnect
Since it also appears you've made an attempt at just about anything that would normally be suggested I suggest a "clean slate day." Take some time out to go have some fun, just the two of you to get re-connected. Spend all day together, starting with a breakfast out. Do some silly things during your day as well as some serious. Take a walk in the park, go to a matinee or your daughter's favorite sporting event, go have a spa experience together (even just get both of you a shampoo and trim, but make it feel like a big-girl spa experience) or whatever seems it would suit your fancy as well as hers. While you are out, at a relaxed moment, talk about it.
"honey, I've been feeling like we've lost our connection and I want to get it back because I love you so much and want everything that is best for you. What do you think about that?" (or something like it) See what she says - you may need to be quiet for some time. She is probably feeling the frustration too so when she does share, just listen and paraphrase.
When You Get Back To Reality
It is time to be consistent. Pick one method to use with her (or an appropriate combination of methods) and then stick with it. Getting used to a new type of discipline often takes time, so switching from one to another abruptly or too often can actually be confusing.
I recommend combining choices (as in the Love and Logic Method) with natural consequences. I know you've already tried each of these, but both can be a bit tricky - especially to do consistently - and tough to switch to. If you give it time - especially with the support of others around you though, I think you will find it will work wonders. Spend some time really getting to know the Love and Logic Method. You can probably find these books at the library if you don't want to buy them but there are some commonly made mistakes (like giving one choice and a threat that isn't really a choice) and things to avoid that can undermine your efforts.
I did offer my daughter one additional layer after she hit five and started to do the same thing as yours for a little while - "but I don't like either choice." I felt it was a good transition and everyone should know how to compromise so I taught my daughter about "win-win solutions." You can point out that if she doesn't like the choices you have offered, she can offer another win-win solution, choose the option she can tolerate most, or continue to whine and let you choose for her (which officially would fall into that "threat" category, but it worked for us). With my daughter, if she simply whined about her choices, I just said, in a matter-of-fact tone, not with any frustration or anger, "well, what would you offer then?" At first her ideas were often she wins, I lose ideas, but I'll give you an example of how an exchange like this went:
"But mom, I don't like either of those outfits."
"Well, what would you choose?"
"this shirt (short-sleeved), A skirt and my flip flops"
"That would be really cute if it was going to be an 80 degree day, but
as it might snow today, I can't be on board with that choice. Can you
find a win-win solution?"
"What if I wear leggings under the skirt, and a hoodie?"
"That sounds alright by me if you also add warmer shoes and keep the
"but mom, I was in the middle of a game and don't want to set the
table, or feed the dog."
"I understand you are in the middle of a game. You choose which chore
you want to do (set the table, or feed the dog) and I'll give you two
more minutes to play before you have to actually do the chore - that
way you can get to a good stopping place."
"I've offered a win-win solution so at this point, you can offer up an
equally good compromise, take my suggestion, or I'll choose one of the
original options for you. You may not continue to argue and whine."
When she forced me to make the choice, I always chose what I knew would be her least favorite option. Once she learned that she probably wouldn't like my choices, she had motivation to choose something more of a compromise. Eventually, I was able to say, "What's your win-win solution?"
Obviously, you can't always allow for choice - in those moments, if you have honestly offered plenty of opportunities for her to choose things at other times and be in control at other times, you can pull the parent card, "honey, I let you choose a lot, you're just going to have to trust me on this one."
However, I see the love and logic method as more of a preventative than a total discipline solution. By offering your daughter ample opportunities to be in control (respectfully and with her developmental status in consideration), you diminish the number of arguments and fights over-time, but there are still times when kids make mistakes, are outwardly disrespectful, or need a lesson. This is where the natural consequences come in.
With natural consequences it is critical not to warn!!! Commonly parents warn their kids about the inevitable consequence of their actions. Then, when the consequence is apparent, the child sees it as a punishment offered up by the parent rather than as a consequence of the child's own choices. It may seem cold to simply allow a child to suffer X consequence when you saw it coming and might have saved them the trouble, but it really is a form of love to allow them to reasonably learn from their own mistakes.
For example, with teens, parents frequently warn their kids, "If you don't get your report done during the week, you won't be able to go to that party Saturday Night." (or something akin to it anyway). Instead, something like, "How is your report coming?" followed by, "Oh you haven't gotten started yet? Hmm. I hope that works out for you" will remind your child kindly of what it is that needs doing, without making any threats. Then, when Saturday comes and the project isn't yet finished and the child misses out you can honestly just say, "Bummer - I wish you could go too, I know you were looking forward to that party. I'm so sad that you didn't get the project done." And honestly know you are sad with your child but standing by the value of getting first things done first and allowing your child to suffer the consequences of their own choices.
Along with Love and Logic, I also almost always recommend "The Seven Habits of Highly Effective Families" for situations like this - not because it outlines a specific discipline plan, but because it offers a really helpful outlook on running the business of a family - including discipline and structures the whole thing around seven habits critical to success (like working well with others through seeking out win-win solutions).
In regard to dealing with the tantrums - she will throw them for awhile even after swtiching tactics with her. Kids are resistent to changes, and despite the fact that they crave and need structure - they resist it too - it is part of the job of being a kid it would seem. In terms of dealing with the tantrums, there a number of great resources right here on parenting so let me refer you to these question and answer sets:
Dealing with Tantrums in the Older Child
How do we get our five year old to control his temper and behave?
12 year old with temper tantrums - help needed
How do you Teach a Stubborn Eight Year Old, Mum and Dad are in Charge This one is less about tantrums and more about how to speak with your kid - I'll grant it is for an older child, but again, may offer some more helpful ideas as well.
This last one is on a different topic and refers you to my answer to the question, but it directly addresses tantrums in the child in the question and may also have some useful info on apply natural consequences to tantrums when they arise as well as a small amount of prevention.
Seeking Help from a Professional
Last but not least, there is nothing wrong with seeking professional help family counselors can be an amazing resource and whether you use your sessions to reconnect or to get to the bottom of behavioral issues (or both) it certainly won't hurt to go see some one.
I wish you well, and please let us know how it goes.
I'm sorry this answer is so long, but I hope it helps.