Hello L.,
I am 24 years old, married, and have two daughters...three years and 18 months, am paying bills, and rent. I think $50 and a few chores is a tiny price to pay for what she's getting. I mean...she gets the comfort of home, doesn't have to buy groceries, pay the electric and all other bills, and has the freedom to concentrate on school and work without any major additional responsibility (kids, mortgage, keeping a marriage healthy).
If anything you are helping her build character and learn a little responsibility. I wish my father forced me to save money when I was young. Granted I got married and moved out when I was 20 but I could have used the extra cash.
As far as her room goes...just close the door. That's what my dad did. If I needed clean clothes that was my problem! It's hard to keep it clean when you are running around in the morning getting ready for school or work. I was the exact same way. My room looked like a laundromat exploded. It should go away once she has her own place.
When it comes to other chores...that may take some convincing. Try asking nicely and explaining that you need a little help.
As far as her wanting to escape on the weekends...I think it would be reasonable for her to leave one or two weekends a month. It's not fair to ask her to totally give up all her friends. But she should know that trips like that cost money which she should be saving! Maybe you all can work out some sort of deal. Let's face it, if she doesn't learn to save money now she never will.
Want an example? My brother and his wife are $30,000 in debt because they would rather have taken trips and spent money on things they didn't need rather than putting it in the bank. Of course it doesn't help that his wife is allergic to work.
I could go on and on with other examples for you but I won't.
You need to be firm with her, she needs to learn how the real world works.
Sorry this was so long. I really hope things work out for you. Send a message if you need to talk more.