Except that this isn't a job. This is a sport that is being played by 11 year olds. Whose parents are paying the coach to coach his daughters. The OP is not paying the girls to produce wins for him.
Cut the girl. But if I was on a team that considered itself a 'family team' that had been together for a number of years and then it changed I would be quite put out. I'm the type of person that is loyal to the point of stupidity. If my child was good enough I'd also start looking for another team for my child. If it's going to be a team that is cut throat and isn't about loyalty but about the best players, then I'll put her on the best team I can find. Not the one that is a B team.
It is a lesson in life.
The coach isn't paying the players. But in all honesty the parents are and are footing the bill to help the player. He's tried to provide an opportunity. The player and her family have settled for mediocrity. The coach is ready to move on and provided a better opportunity. He is being loyal to the players that want to step it up.