What country is this all occurring in? How old is this boy?
The mother is a mess, no doubt about it. There is a lot of passive aggressive stuff going on in the father's behavior that should be straightened out by the court. Here in Texas if you can't work it out yourselves, you HAVE to follow the state mandated formula regarding support and visitation in the divorce settlement. Parents can be held in contempt, can be fined, or put in jail. The threat is real enough to bring a lot of deadbeats around. And certainly, the new wife of the ex shouldn't be able to call the shots regarding contact. Sounds like something out of "Babes in the Woods."
The mother's depression is clear, no time, lots of stress. The child is acting out and the parents don't seem to get it, so it will get worse. Best thing she could do is (if he won't move closer to her) to move close to the father and insist on regular contact and reasonable support. Put the kids first. It's a horrible time to try to start another personal relationship of her own. Just what she needs--another needy person in her life. Make a few lists, prioritize, dump some excess baggage. And stop drinking. Self-medicating is the worst thing she can do at this point.