She's 17 and perfectly capable of moving out on her own, am I wrong to ask her to stay at home?

As a 19 year old all I ever wanted was my parents to support my dreams, they always made me do things I wasn't happy with. They are finally supporting my dream. I understand it might be hard to let go but the best thing you can do is let her be free to soar. You should be happy to see her succeed because of your good work raising her :)