I do think that is the best place right now. I’m glad that you set up some ground rules about the boyfriend, she may not agree, but I think they do need to see if it a healthy relationship.
Is the car in her name only? If it isn’t and you or your ex are on it, I would insist that he not drive it. Not sure of his driving record–that can be easily obtained through public record. If his record isn’t good, the insurance co could refuse to pay if he gets into an accident.
Could she do parenting classes, CPR, college online or even volunteer work? Then she wouldn’t be sitting around doing nothing and she would be learning or helping out.
Interesting about his family. Perhaps they think you will withhold all visitation with the family if they don’t show support–I’ve seen this happen many times.