Getting rid of athletes will hurt your program, even if they are "slackers". Unless they're seeking to cause trouble or harm others, numbers are always a good thing. You never know when one of your hard workers may get injured, and a "slacker" may need to step in their place.
Different athletes adapt to different coaching styles. In high school, I did not respond well to punishment. The more my high school coach tried to punish me, the less I would care and the less I would try. This attitude is so common amongst athletes this age. Now that I've been through several years of college, I look back on those days and cringe. At the time, though, I didn't know the difference. Some athletes let their pride get in the way of a negative coaching style, and some coaches let their pride get in the way of losing athletes. I know a coach who had eight seniors quit her national championship team the month of nationals. Both the coach and athletes didn't want to be the one to swallow their pride and acted like it was no big deal. From the conversations I had with the athletes and coach, both sides were hurting tremendously. Neither side really wins there.
As the coach, you're faced with a dilemma: play Mr. Tough guy and lose athletes, or give in and have them walk all over you? It's a tough one to balance, and I had the SAME experiences with coaching and working summer camp staff, and honestly didn't see the issue until taking some of my education courses in college:
I suffered a semester of a BORING discipline class. The text was so dry, but I was really able to apply it to the classroom and coaching: the golden term is POSITIVE REINFORCEMENT. Recognize and reward the athletes who are doing what they should be doing. It sounds cheezy, but go to Target and stock up on dollar bin items. If one group is constantly nailing the stunt sequence, reward them with a small gift and allow them to help other stunt groups get the stunt down. It creates a "leadership" atmosphere, rather than a "haha I'm better than you and we sit out while you suffer" feeling. Don't do it all the time, or it will turn into bribery and they will expect something all the time. At the end of the week, make sure ALL of your athletes have been recognized somehow. Even the laziest girl, who can't lift a stunt, may be a star tumbler. Have her help another girl with her back handspring. When kids are put into brief leadership positions, and are recognized, they will feel better and want to work harder for you. The brats are the ones who need extra TLC!
Of course, there are times when we have to punish athletes, but make sure it's not a select few athletes all the time. Singling an athlete out really embarrasses them and does not make them want to work harder. If they whole team must do something as a punishment, don't say it's because of "so-and-so's stunt group". High school girls LOVE the blame game and may start petty drama.
Good luck! This age of athletes is tough. You're doing the right thing by asking the board for help--- so many coaches would have just given up by now! Just keep trying and give them a little extra love (even when they don't deserve it) ;)