Your father is lying. He's had physical relations with the other woman guaranteed.
Yes, now that the affair has been exposed, it's up to your parents to work it out. Unless your dad comes clean and quits seeing the slut, they don't have a chance. It's not your fault. It's not your mother's fault. It is your father's lack of integrity, honesty, and complete and utter selfishness that has gotten them to this point. If he had a problem with your mom, he could have discussed it with her and gotten out of the marriage before he brought another woman into the picture.
Check out some of the other forums on the internet. Search infidelity, adultery and lying. MarriageBuilders, SurvivingInfidelity, etc. Your mom could use somebody to talk to to that has lived through this devastation. She is hurt and devastated. Some marriages make it through this, but only if the wayward spouse is an open book. Otherwise, forget it. Your dad's anger does not sound good.
Good luck Anduin. I know this is hard. I've been through it with my parents. They are working through it and sometimes I wish they never got married and I never existed. It can be hard. They are doing better. It's been almost 4 years though. Not an overnight process.