I've been a doula in Tucson for over a decade now.
My experiences do not mimic Swell's or Sunday's. I much prefer TMC over UMC. Northwest is also a great hospital for giving birth. St. Joe's is good, but they don't do VBAC. However, they are one of two local hospitals that have telemetry monitoring, so I give them an extra point for that. I've had two of my 3 babies at TMC, one at Northwest.
However, both TMC and UMC will separate mom and baby when mom is moved to her postpartum room. Average time apart can be 2+ hours depending on how busy they are. Dad/Partner can go with baby, but they still separate. Of course as with anything it is possible to avoid this if baby is fine, but it takes a lot of advocacy.
If you want to avoid separation entirely and not have to do a lot of advocacy to keep baby with you for that time, then Northwest Women's Center is a viable alternative. Baby is checked briefly in the nursery as mom is undergoing repair, and then mom and baby are reunited in the post-op recovery room and stay together from there unless there is something wrong with the baby.