Your son is 13 and should be able to have a major say in where he lives and with whom.
Keep all emails from her where she is violating your agreement such as refusing to allow your son to visit and claiming you owe her money for bills she is refusing to give you. My ex claimed I owed her money for bills that she never gave me and we told that there was no way I could pay a bill that I had never seen. Bills were never produced and that was the end of that subject.
Sounds like you have a stable home with a wife that is willing to help with this situation, not that you couldn’t do it yourself. Just something that will be looked at.
One major issue that you can use to your advantage is the health issue. With her smoking and you living in an area that would be much better for your son’s asmtha, you can use this to your advantage. Also the fact that she won’t use available health insurance should play against her.
Sounds like she is playing the parasite and just looking for more money to support her non-working lifestyle. I say , if your relationship with your son is good and he is willing to make the change, go for it.