That is actually a common restriction with a lot of agencies, as a way of protecting their investment in you. The agency would lose money on you if you jumped ship to take a position at the facility (you wouldn't be working for the agency anymore), so in your employment agreement with the agency, you promise not to work for the facility for a year after your last assignment there; if you do go to work for them sooner that that, then Maxim would be entitled to monetary compensation. I think it's called a non-compete clause.
My agency has a similar clause: if I violated it, would have to give them 25% of my salary at the new facility. This is no problem for me as I don't want to be a permanent employee of the site I get sent to
You would not be breaking any law if you decided to quit Maxim and work for this hospital directly. Also, Maxim can NOT prevent you from earning a livelihood. However, Maxim may decide to go after you in court to enforce this restriction and collect that money.
If you're serious about leaving Maxim for this hospital, you should have an attorney look over the agreement you signed with Maxim. You may also want to keep that lawyer handy should Maxim threaten you with legal proceedings. And that's all I can tell you as we can't give legal advice.