Some backstory
The father of my child - I'll call him Bob - and I met when I was a freshman in college. We dated for 4 years and in that time he never got along with my parents. They were either "demeaning" or "disrespectful" and I had quite a few fights with them for my independence during that time. After we had been dating about 3 years, I got pregnant and that caused all sorts of issues. My parents, who are traditional Catholics, were appalled and angry and insisted that we get married. "Bob" was furious at them for their reaction. We never got married (thank God) and ended up splitting up a year later for a variety of reasons.
My parents and I have had our set of issues over the years, as I fought for my independence, and after I got pregnant, we went almost a full year not talking. Now (two years after my daughter was born), our relationship has finally started to mend and I have been speaking to them more and more frequently.
Bob and I get along now, and he has begun taking on a lot more responsibility as a parent since we broke up (he never did anything while we were together). I am pleased with this, because I would love to see my daughter grow up with a loving father. We have a pretty civil relationship and don't fight about anything really. My daughter spends half the week with him and half the week with me and we split costs 50/50 on everything.
The Problem
Bob still hates my parents. He hates them so much, he gets mad just talking about them. He insists that he never wants to see them again, and he doesn't want our daughter to spend any time with them. After he found out that my parents and I were mending our relationship, he was pretty upset because it meant that our daughter would be around them.
He finally agreed that it was okay for her to be around them, as long as I was there to constantly supervise. However, according to him, I'm not allowed to ever leave her alone with them, and they definitely can't babysit.
This seems unfair since his mother gets to watch our daughter all the time. I have an excellent relationship with Bob's mother and I talk to her even more frequently Bob. I would never let her out of my daughter's life, because they are both so happy when they spend time together. I still don't find it fair that she should be allowed to watch my daughter, while my parents are essentially banned from this.
My parents have begged for the opportunity to watch my daughter since our relationship has healed and I would love to let them do this. Sure, there are things they overreacted about when I was younger, but they've been working on this, and they are good people with good hearts. However, I'm scared of shifting the balance so that Bob and I can't be civil anymore.
I feel like his anger is completely irrational an I don't know how to deal with this. Does anyone have any advice?
NOTE: I can't give exact reasons why Bob hates my parents so much, because I've never fully understood the hate. I know that while we were dating my parents disliked him in the typical "no boy will ever be good enough for my daughter" way, and I think he may have taken this personally. They also always wanted me to visit them (once a week while I was in college), and Bob thought they were unreasonable and overbearing. He hated how they would send me on guilt trips whenever I would tell them I couldn't visit because I was doing things with friends instead. He also hated that they never helped me with money even though they were very well off, and I was forced to work full time to pay for tuition, rent, and other living expenses while I was in school. I understood some of the reasons he was mad at the time, but the fact that he still holds these grudges just doesn't make any sense to me.