8 Hours to decide: Basketball or Winter Training Grind?

I go to an extremely small school in a rural area. Our track and cross country teams are not that good, but I've worked to build myself into a decent/slightly above average runner over the years since middle school.

I'm a female junior with an xc PR of 18:02 and track PR's of 5:19 and 11:49, but I split an 11;22 the last race I was at for XC.

Anyway, I don't know whether or not I should take basketball season off to focus on rehabbing a muscle disparity I have in my shoulder as well as cross training and running, or if I should do basketball.

I want to do basketball because it's fun and social, and if I don't, my parents will control my training in the months leading up to outdoor track. I love running and care about it so much, and one of the ways my parents punish me is by taking away exercise/training. So I'll have to be on my best behavior to avoid ticking them off for 4 months.

Why will my parents control my training? Well, I have a history of anorexia that landed me in a treatment center going into freshman year. They think I run just to satisfy the disorder. Additionally, they don't want me to burn out or get hurt.

I want to run D2 in college and be the absolute best runner I can be. It's a toss up. What should I do?