Hi,
Sounds like a tough situation! I would definitely not give up on the lab especially if you don't have the other hospital position yet. You may have to volunteer for three different things and then pick and choose. It's never a bad thing to do multiple things, especially related to research. If you really want to quit one, think about who can get you far in terms of application, letter of rec., etc. If you are not planning on taking two years off, you will not get to know the hospital supervisor well enough for him to write you a solid letter of rec. In my personal experience, it takes at least a year of working with someone for them to really get to know you.
I would encourage you to try to get on a poster, presentation, or paper in your current lab. Even if you quit, let them know that you want to work on such things after you leave. I left my lab but remotely worked on a paper for a while. Hope this helps and best of luck! I know this process is rough.