How do you get comfortable with someone who is friends with someone you can't stand?

I have wonderful cousins who are close friends with my bio-dad and his family, whom have never been in my life. Actually it goes further than that, and he’s been pretty ugly to my mom, and indirectly to me.

Recently I learned that my cousin house-sits for him, and my other cousin is best friends with my half-sister.

What I have been doing is ‘pretending’ I don’t know the things I know so things aren’t too stressful for me and my cousins to remain friends and in each other’s lives (we have a great time together.)

The thing is, pretending is getting more and more difficult, and sometimes they slip up and say things they seem to ‘hope’ I didn’t catch, but I do and it’s hurtful.

I should also mention my mom and my husband both love this group of cousins, as do I, so apparently I am the only one feeling some resentment here. And it drives a wedge in friendly relations because I’m now finding myself making excuses not to be around them, which is confusing mom and hubby.

What would you do? I’m tired of being hurt by this same situation with my dad over and over again.
People have said, you need to just get over it and not worry about it anymore, but when it affects your life so much, how do you do that?