Gay Parent Invite

I`m looking forward to a wonderful future with a perfect man that my parents both adore. I`m very close with my mother and father however, they are not close at all.
3 years ago they went through a bitter divorce and my father revealed that he was gay and has had a steady partner for some time. My mother is unfortunately a bit homophobic and is hurt and disgusted by my father`s lies and cheating.
He`s not a fan of her`s either.
My problem is inviting them to my wedding. Like I said, my fiance and I are both close to my father and his partner, and close to my mother and her family. No one knows of my father`s situation except for my mother, finance and I. No one on either side of either family is aware of the situation. I`m not sure our wedding day would be a good time for everyone to find out.
I would like everyone to attend the wedding but my father has announced that he will not go unless his partner is invited and my mother announced that she will not attend if my father`s partner is there.

Any suggestions on how to handle this?