@Kiraz123,
I don't know how old you are, I am going to assume that you are a teenager in high school (although my basic point would be the same anyway). My parents divorced when I was in high school, and I am myself divorced.
Divorce sucks for kids. I am sorry about this.
My advice is that you do nothing. Your parents are responsible for their marriage. Your parents are responsible for whatever is happening between them. You shouldn't be in the middle of this. It is not your place, or your responsibility, to be getting between your mom or dad or to judge either one of them. If you tell your mom what your dad is doing, you are putting yourself right in the middle of their screwed up marriage. That isn't fair to you.
If you are angry with your dad (which you have every right to be) you can tell him clearly that you want nothing to do with this woman. You might even talk to him and tell him that you are upset. This is fair.
But your dad is correct in one sense. You have no right to be looking at his phone. Anything you saw on his phone is not your business. You shouldn't be in the position of judging your parents.