I'm going to tell my dad that my mom was talking to another guy
Did you see it or did someone tell you about your mom?
I have friends telling me the same thing about my mom, so I want to know if it's true.
While you didn't see it, it is not good to flirt if you are married. You should find out the truth and let your father know so that they can resolve the problem together or separate.
No, I want to prove that this is all true and that my mom is unfaithful.
Your concern for your family is commendable, but it is all still just rumors. You can't be sure about it with just hearsay, and your dad could be really hurt by all of this, especially if it isn't true.