Oh my gosh, your mother and my mother were besties. My mom signed me up for swimming class - twice - knowing I was terrified beyond all reason of water (because my father had nearly drowned me at age three). When I very predictably panicked and quit, that was held over my head in the same way - "you quit everything." I quit what I never wanted to do in the first place, yes. I also quit band, admittedly, but a) I was out sick for one week, the week the teacher apparently explained how to read music, and he never explained it to me after, so, frustrating - and b) I didn't get to play the instrument I really wanted to play because it was too expensive to rent. And again, I was 8. But "you're a quitter" and refusal to do things for that reason ever after. "You're a waste of money" was another mantra.
And besides - kids are supposed to experiment. How else are they to find what lights their fire in life?
So, what kind of game? Board game, I recommend getting a big cardboard and colored pencils. We totally did that as teens. Computer game, I'd bet there are teach-kids-to-code type programs, but I don't know about cost. GREAT work on the STEM camp and horse riding!!