I don't think it's wrong for you to want a relationship with your dad, but it is weird that you kind of brush over the cheating. Your father had an affair, does that not affect you? You don't even look at him a little different? Do you not understand why your mom is lashing out or why she's as hurt as she is? Again, I do not think her request is reasonable, but this woman, from what I'm getting from the post, was cheated on, publicly enough that it was a big scandal, lost her husband, her home, and her son. While everyone is having a great time with the mistress, she's seemingly alone with no one in her corner telling her how what she went through was hurtful and offering her some comfort. You're like, "he's my best friend, so I don't really care, him cheating on my mother didn't change anything to me, it's not like he cheated on me."
Relationships are complicated. I don't know what your relationship with your mom is, but if she wasn't abusive and you do have some affection for her (even if she isn't your best friend), I would talk to her. Both of you should explain how you're feeling. Maybe she wants you with her because she thinks you like being around her as much as she likes being around you, maybe she thinks you two are closer than you actually are, or maybe she's nuts and is making one final attempt to control. But your mom as seemingly lost everything important to her by putting her foot down against cheating while everyone is like, "finally, she's gone. Just swap her out with a younger version." I don't know a lot of people who wouldn't be hurt by that.