Re: Do most hospitals have daycare?
If I were you I would try to find a nanny/babysitter that will come to your home. This might be an ideal job for someone going to college, you could probably even try talking to the child development department at a local college to see if you could post an ad or if they have anyone they recommend.
If your nursing that may make a hospital day care better, I've never heard of one being 24 hours.
My husband and I both used to work long and crazy hours. I just really preferred the kids being able to stay with their routine of sleeping in their beds, waking up at home and having their own belongings. I am fortunate that I live in Oregon where daycare is cheaper so I used to pay $7/hour for 3 kids. So I guess the going rate in your area will also make a difference of whether a nanny/babysitter is an option.
Good luck finding daycare that will work.