I grew up in Carrollton, so when the hospital first opened way back when, everyone was very excited to have a new hospital so close to us. However, I've had a few experiences there that weren't so great and have heard a couple of horror stories from others, but everything bad has always been about the ER (like one of the other posts states, as well).
There are some good doctors out of Trinity, though. Ceazar Aleman is one of them. My sister used to work for him & my mom used to do his billing. I also used to see OBGyn from Trinity - Frederick Crutzman. I guess he was an ok doc, but his bedside manners pretty much stunk.
Never have heard anything about deliveries though, so I can't give you any info on that.
Trinity Medical and RHD Memorial Hospital (used to be called Deadman Hospital years ago...guess they finally realized it was a bad name for a Hospital!) are sister hospitals that are run by TENET. I worked for the Marketing Department once at RHD Memorial Hospital. There were a lot of positive advancements going on at the time for both of these facilities, so there's some more positive feedback for you.
You may try posting the doc's name that you'd be using. Chances are he may practice at another hospital & maybe someone has info for you on him/her specifically. That has always helped me in making decisions like these.
Good luck!