I know he merely tolerates me and my family activities. He thinks that the chores he does for me, for which he earns a healthy allowance, are slavery. He thinks limits on internet time and expectations around his grades are grossly unfair.
I doubt it....this is a "thing" that all teenagers try on. It's a rite of passage. I don't think your relationship is fractured, or not as much as you feel it is. Kids like rules, but they must try to convince adults otherwise. Life without rules and structure is actually extremely stressful to teenagers.
Right now his father's house seems like a vacation. Sure that has its attractions. I agree with the suggestion above...unless the court documents allow your son to change his living situation as he desires, set up some structure where he can spend extended time at his father's house and get his fill of it, but not move there and not change schools.