This is devastating for any kid. You did the right thing to talk to your mother. She does need to talk to your father. A marriage is rarely improved when one of the partners has an affair. A marriage is often improved with counseling.
At this point, all you can do is insist that your mom tell your dad. You should not have to hold a secret that is this painful to you. Tell your mom that it is just too hard for you to keep her secret when you know she is hurting the father you love. Go back to your original statement — that she needs to tell him or you will talk to him about your suspicions. If she suggests you will be to blame for ending the marriage, please don’t accept that idea. She is the one who is violating her marriage vows, not you.
Then get out of it. The state of their marriage is up to them. Whatever happens between them, they can each still have a loving and honest relationship with you. Focus on your relationship with each of them and leave them to figure out what to do about their marriage.
I wish you well.