What would you do? Hospital birth insurance question?

So the hospital in my town is no longer taking the insurance I have. My OB told me to call and switch my insurance group to another group. So I called and requested to switch it. I waited like 2-3 weeks for them to get back to me. They finally did and said they can not make the switch. They sent a letter saying that they will cover for me to give birth at that hospital. So I called the hospital and spoke with billing and asked and he wasn’t sure if they would take it for labor and delivery. He said they only take it for emergency. He was not sure abt labor and delivery. He said there could be a chance they could bill me. Now I have no idea what to do. I could literally give birth any day now being almost 38 weeks. I tried calling my OB abt the issue but was put on hold then voicemail. There’s another hospital 30 mins away that will take the insurance and I had my first there. Can I just go straight there if I do go into labor? Or would I have to find an OB in that city to give birth in that city?