When our daughter was born, my water broke, but I never went into active labor, even with drugs. I didn't dilate past 3 cm. When her heart rate started to drop about 13 hours after my water broke they decided to do a c-section. When they gave me the spinal the only thing that got numb was my feet. So, they put me completely out.
When I was pregnant with our son I wanted to do VBAC. The hospital (Mayo both times) was ok with me trying because they couldn't find an exact reason I had problems with my first except that our daughter was face up.
My labor was very similar to my first. My water broke, started labor right away this time, but never dilated past 4 cm. Our son started taking longer and longer for his heart rate to recover after contractions so they decided to do another c-section. My spinal worked so I was awake for our son's birth, but I had to be put out to finish closing me up because the spinal started to wear off. The cord had been wrapped around his neck and that was probably why his heart rate was affected.
From my experience, I'm guessing that if they can see a specific reason why a vaginal delivery wasn't possible, they might not agree to a VBAC even at another hospital. My sister-in-law also had a similar experience with our niece. She was told that her pelvic opening was too small and that a VBAC would not be possible.
Talk with your doctor and a doctor at another hospital. Be sure both look closely at all the medical records from your first baby. They will help you decide what will be best for you and your baby. Good luck!