There's no easy answer here - someone will lose out on the day.
I've been dumped and two timed, pretty shitty to go through. But I also had a best friend 'dump' me, and out of all the men who dumped me our friendship breakup was by far the hardest and worst to get over. It's no lie to tell you that I'm very hesitant about making female friends even now, 20 years on because of the way she ditched me because her boyfriend of the time didn't like me. I can't imagine how much more awful it could have been if she'd betrayed the friendship and destroyed my marriage in the process. Even now when I think of that friend and the way she hurt me, my stomach lurches in a way it never did for the men who two timed me.
I'd like to think that I could suck it up, be fabulous at my child's wedding and be civil to an ex who cheated. After all, the priority is the person we created together. And in some ways, showing your ex you living your best life and all that could be quite nice for the ego.
I would want to be civil to ex friend in a situation like this but oh, honestly with the best will in the world, I don't know that I could. It's like, you know the odds on your partner leaving you for an OW might be high statistically or a relationship not working out, but a best friend fucking you over is just not something you expect or ever assume you'll have to face really.
The most diplomatic outcome is that your dad insists to you that he's happy to attend alone or to bring a friend rather than his wife, and that she would also understand that the bridges she burned 10 years ago remain burned.
Wishing you a wonderful wedding day, which ever way it turns out for you.