I agree that your DD should get some circle time, but I am 98.2% sure there is no way your DD will get enough circle time to make you happy, so the best thing you can do is find another team (more competitive, older age group) or start your own...
98.2% wrong. I don't view asking for 1-2 innings in a scrimmage as burdensome, especially when you played 8 innings and used a different pitcher every inning. I certainly don't feel like asking to pitch 3 innings in a league where you play 3 games on a Saturday (usually get 15-18 innings in) is asking too much either. I never asked for her to get a majority of the work. I just asked her to get some work as opposed to none.
At the end of the day, it's DD's decision to stay or go. While I have a long-term view of where I would like her to be, it's still her journey. She's only 10, right now she just wants to play with her friends. I don't want to take her away from that even if it means 6-8 months of stagnation (and I don't even know if it does mean stagnation).