Ditto PP. If you want to deliver at this other hospital, you should find a provider who has privileges to deliver at that hospital.
If you were to show up at the other hospital, without any proof of pre-natal care, you will be treated as such. Meaning, you'll likely be subject to an IV, IV fluids, IV antibiotics, continuous monitoring, etc. It's also possible that this other hospital and their providers don't take your insurance. Birth is expensive in the hospital, so make sure that your insurance is accepted first.