I have a child of 17. My child is naturally athletic, ahem..like their father..er..umm. SORRY! I get a little proud of my child sometimes [ also a WTBTS no-no. too much pride and all that..] I had to make time to play with my child because there were not always other children around. Bike rides, tennis, playing catch, wrestling around. Those are all great things to do. Children really do need to play every day, but not to the extreme.
I understand that you want your child to interact with other kids. Do they play sports at school? Sometimes you can get a clue about what they like that way. My kid wouldn't talk about too much, except soccer and volleyball. That told me what they were interested in. Are they a little shy? It can be intimidating to play with other kids after a certain age. Cliques start forming early in school, and kids get labeled. A JW kid has another strike against them, so it can be difficult getting them out of their shell.
I will say that being physically active is very important. I see so, so many young JWs that are overweight, or even obese. That is not a great start in life. You would think a religion that promotes respect for life would show respect for the health of their children. Sure, the Awake has had a couple of paultry articles about healthy activities, but then the GB turn around and make that lifestyle an impossibility due to the endless JW treadmill.
I am sure you have it rough with full custody, and have stress of your own. Maybe you two can find something that you both like to do? That may be a good starting place, a warm-up if you will. Just have fun and see what happens.
DD