I guess you have to prioritize, and figure out what's your responsibility and what isn't.
You say that she moved in because it was "safer" - can you elaborate more? If she was in an unsafe home with violence, drugs or major instability, that's one thing. If it's a general "suburbs are safer than Chicago", that's another.
I believe it's up to her to decide if she's going to school or working. You're not her parents, and she's 20 anyway, so it's her call. Offering her money (and her father-in-law doing the same) as a "bribe" to go to school usually backfires. She's working (and by your admission, working hard), and she has tons of cash on hand. She has no expenses so she has plenty of party money.
It's also not up to her to set an example for your children. They are 13, and while you don't want them to experience all adult issues, you can't shield them entirely from everything.
Whether you approve of her drinking is irrelevant because you aren't her parents. Yes, it's illegal, but I think we'd be hard-pressed to find 20 year olds who don't drink. I'd be more concerned if she came from an unstable home situation and has no info on pregnancy prevention, sexually transmitted diseases, and so on. Of course, that's not your official responsibility either, but as a caring aunt, you might inquire about her safety. Otherwise, she's a typical 20-something reacting to intense freedom.
That said, you don't have to turn your lives upside down for someone who isn't there, isn't helping and isn't paying rent. You're giving her a place to crash on occasion when she shows up, letting her shower and do laundry. That's plenty, for free. So your kids have to share a room because she's there? But she's not there anymore? So, you find a nice corner of the house with a decorative screen to pile up her stuff, or give her a spare dresser in a guest room or a corner of the family room, and you give your kids their rooms back. If she wants to crash with you 2 nights a week, she can sleep on the couch or a blow-up air mattress in the family room. She doesn't get to lay claim to an entire room she's not in.
Then, if she continues to mooch of you with no chores and no responsibilities, you either charge her a nominal rent for losing, laundry, utilities and storage, or you give her a date to find her own place. She wants to be an adult and stay with friends and work full time and drink? Fine, she can have the adult responsibilities that go with it - which include a paycheck that isn't yours to spend on clothes and movies, but to support your food, clothing and shelter.
So, depending on her home situation, you either consult with her parents, or you make your own decision. The deal was that she would go to school. She does not have to continue that just because you think education is important - so take that off your list! She wants to be an adult, then she becomes one. So that means she pays rent (so you can pay someone else to help your kids with homework and shuttle them to the activities you can't get them to) and to cover what you pay on her behalf, or she moves out, which is NOT "kicking her out on the street."
You must, not matter what, put your value judgments about who she sleeps with or what she drinks, aside. You may well be right, but just isn't your call. But you can certainly take control of your own home with an adult discussion with her about adult matters.