I am the commissioner of my son's basketball league. First you should check the website for YMCA most leagues have a player participation rule. I looked at the rules for Arlington (TX) their rule: Every player that shows up for the game on-time shall play a minimum of 2 quarters per game.
Please read over the rules and talk to the coach, if nothing happens then talk to the YMCA representative incharge of basketball.
Good luck this season not all coaches are hard to get along with.