Find a way to do similar exercises at home... Most the equipment you use at the gym is to do exercises you could already do at home, get creative, climb up and down some stairs, jog, lift heavy household items etc.
Yeah, what Tony said. However, if the issue isn't specifically with the gym, curfew related, or otherwise related to your leaving the house, maybe you could discuss an alternative consequence. Be willing to accept no for an answer, in other words, don't whine, beg or pout. Imagine how mature they'll think you are if you handle yourself well. Money in the bank. Good luck.