Her parents have told her the only way to get happy again is make sure I am totally out of her life and the kids lives.
Well Mommy and Daddy are going to be disappointed, because unless you have been physically or emotionally abusive (based on facts and not on just heresay) the only one who can remove you from your kids lives is YOU. Do not give up your rights. As you describe your in-laws they seem like arrogant, evil, and manipulating people.
Sorry you are going through this, but in your case specifically you have to be careful with EVERY thing you do and don't do. Keep the scheduled phone calls, don't give them the opportunity to say you haven't made an effort to contact your kids. If I was you, I'd still make plans to get down there to at least visit them on a long weekend. Just to make sure you stay in the picture.