You can put a distance on how far a parent can move with a child, but I don't know if you can if he just has visitation rights. As far as who he lives with, I would arrange some kind of meeting and the father's new place with the friend being there, just so you can see the living enviroment. If you don't like what you see, you could always try to get visitation set from the mothers and childs home town only, not sure if it will work, but it might. Just don't sign anything until you check everything out, you can even do your back ground check on the guy he is moving in with using the people search online, I think it cost somewhere around $39.00, but it will be worth it to find out if it's a safe place to be for the child. Hope this helps.. Good luck!
