[disjunction]

I don't see the problem. If you wind up seeing her and the kid more frequently, somebody is going to have to keep him under control when the 3 of you are together, and that somebody will have to be you. As long as she is willing to cede you that authority, there is no problem. And she could probably learn by example.

Discussing your authority with her kid is your potential relationship issue, but cross that bridge when you come to it. For now, you are merely observing something that is Not Your Problem.