Since you left out a few details, I'll give my opinion on what I would do. I would stick with my current job for at least 6 months to a year. You have no idea of what the new hospital would be like or what your new coworkers would be like. You don't have a ton of experience and you could potentially wind up on an undesirable unit without a lot of options to leave. I would not leave a good unit this early in my career. And unless your family member is a nurse, they might not be aware of unit politics, dynamics, etc that effect the nursing staff.
I also think financially you would be better off staying put. From what I know about leases, they are considered a contract. If you breach the terms of the contract, usually there is a financially penalty. Given the financial issues you and your family currently face, it seems like the opposite of what is the most sensible.
It is admirable to want to help family, but I would try to get to a more secure place myself before I overhauled my whole life to be someone's care taker. You didn't say if they were going to need help indefinitely or if they have children or in-laws who could help in a pinch. Maybe there are a few more options to consider. Just my two cents.