One thing you don't want to do is move out of the house without your son. And don't let her move out with the kid.

When you file for divorce, file for an ex parte motion asking for temporary custody.

The cheating doesn't matter. Now or then. Don't rely on her parents to testify for you. Blood is thicker than water. They may agree with you, but they will choose their daughter everytime.

What is your work schedule like? Has your stbx stated that she will fight you for custody? How often does she travel due to her work? Keep documenting how often she stays out late. How much time you and she spends with your child.

And get a good attorney.

Edited to add:

Your stbx isn't going to have to ask you to see her child. Regardless of who gets custody, there will be a parenting plan in the court order. If you get custody and refuse to follow it, you will be in contempt of court.

Also, chances are you won't be able to make all of the decisions regarding your child, either. Joint legal is pretty common. What that means is that BOTH of you make the decisions regarding school, religion, childcare, medical decisions. If the two of you can't agree, then you have to go to court and a judge will decide.