I carry one and have a newborn cable/sensor as well as an adult cable/sensor. It's a great addition, because you can document that baby has appropriate oxygenation and perfusion, also handy with those moms who are having that "shortness of breath" sensation but are absolutely fine, and useful with postpartum hemorrhage also.
I know this is an old thread, but no, as of right now anyway, can't do VBACs in a birth center.
I, however, as a homebirth CNM, can do anything within the boundaries of safety and my protocols. I DO tend to adhere to the low-risk screening criteria for Florida LMs, though I am not licensed under their statute, simply because I believe that low-risk women are the ones that should birth at home.