You staying with your dad, at least in your mom's eyes, is you choosing the new chick over her also.
And if thats what you want to do, so be it. But you're actively choosing another woman over your mother.
Think of it like this: Someone was caught doing x. X being any deplorable act you wanna fit in there. Let's say being racist to the point of violence.
Said member of that race who you've hung out with comes to you, tells you what happened, and asks you not continue hanging with said person or else they're going to deem you racist too.
Although you don't have any racist views, and although that person has never been racist to you since your not that "undesirable" race, you continuing the relationship puts you in the racist category.
You could stop the relationship although it hurts. And in doing so you may even help the person learn the errors of thier ways, or atleast the consequences of their actions.
Or you can say nothing and allow the racist tyrad to continue.
Edit: I also want to say I'm sorry your in this position. It sucks you have to make this decision. And although its hard now, I hope everything works out in your favor in the long run.
Truly am sorry
Edit edit: yall don't love your mom's and have her back and thats just sad. Boo me all you want, but if either of my parents was to cheat I'd side with the other until the cheater comes back and apologizes like their the adult their supposed to be.
Hold people to higher standards, especially the ones that are supposed to be raising you