Do you have to deliver at a hospital your doctor is at?

Hello I'm 29 weeks and 2 days with my rainbow baby. There are 3 hospitals in my area right now but only one delivers until October when their l&d unit opens up. I'm due in November so I have the option of either hospital for delivery. The issue is I really want to have a water birth but neither of the hospitals offer it. There is a fourth hospital 45 minutes away that does offer the water birth. My fiance is completely against it though since it is a further distance and my doctor wouldn't deliver our baby. I originally thought I was going to have a C-section due to having a very narrow pelvis but my doctor(private practice so he only is at the hospital 2 days a week) said I need to try to labor her out first and if she gets stuck or reaches 10 pounds then a section will be done. The hospital that is opening the l&d in October does offer a small pool to sit in but from what I understand you cant have the baby in the pool. The hospital my fiance wants me to deliver at is great (and my doctor delivers there) but I just really want to have the baby as natural as possible through a water birth. I am able to relax more it seems when in the tub with warm water. The hospital he likes has a friend that is able to get us some extra things but I honestly just want to be comfortable. I did ask about a home birth and that wasnt really an option either since he worries about the baby getting stuck in my pelvis due to how narrow it is. Any clue if I could go to the hospital 45 minutes away or do I need to go to the one my doctor is at? Any suggestions are welcome as to help.me figure out what is the safest for my baby and me.

Side note: while my mom was pregnant with me she fell and it damaged my hips. They were loose at birth and part of lower end never grew.