Hi C.,
You really have your hands full! I'm sure you're going to college to provide a better life for your family in the future, but I'd suggest maybe you take one class next semester. That way, you're still furthering your education but making more room for your children.
This is a pivotal time for your 11 year old--and your 7 yr old is watching, as is your other daughter. Your oldest (?) probably feels very responsible for a lot of things around the house, whether or not there's a caregiver there. She's figuring out how to turn into an intelligent, popular teenager by herself when she really needs your input, whether she thinks she does or not.
Is her father involved in her life? If he is, does he know how she behaves? What does he do about it? Maybe you and he can sit down with each other and work out a plan that involves her seeing you 2 on the same page concerning every aspect of her life. For example, you should both discipline the same way. You should both have (basically) the same rules at each house. If she's grounded at your house for hitting her sister and it's almost visitation time, the grounding should carry over. His house can't be the opposite of yours. It's too confusing, scary and simply unfair to the children. This also goes for whomever is providing child care while you're at work and school. As for your being divorced, what's done is done: Just move forward with the situation you're in now and make the best of what you have.
If you don't have a good enough relationship with your ex to work out a cooperative interaction that is aimed at creating harmony, safety and respect for your children, seek counseling from her school counselor and from YOUR school counselor. Your counselor (Dean, instructor, anyone you can confide in) will most likely have seen or dealt with a similar situation in their time teaching--seek advice from them. Or go to a clergy person. You can't just throw her away because she's not acting the way you want her to. Of course, to YOU it's not throwing her away, but to an 11 yr old, you're telling her in no uncertain terms that your love has a price and comes with conditions. I know that's not the message you want to send.
Meanwhile, you can start to turn things around immediately. Instead of yelling at her when she acts out, speak with her when there's a calm moment before this happens (and you know it will). Let her know you're changing the rules starting now. If she breaks a rule, she's going to her room, at which point you'll remove her TV, iPod, computer, phone, etc. Keep going until her room is stripped of anything non-essential. She'll get the idea. Be consistent and firm but always keep in mind you're trying to show her how to respectfully resolve conflict so she knows how to do it when she's an adult (and a pre-teen and teenager!) lol Your goal for your actions should be the goal you want for her actions. Don't act one way and get mad if she does the same.
Anyway, I didn't mean to go on and on. I know this is easier said than done, but maybe one suggestion in here will help make your life and your family's life much more pleasant. Your ultimate goal is to raise 3 well-adjusted adults who can handle awkward, tense, and unexpected situations. Now take a deeeeeeeeeeeep breath and move forward!
D.