I always thought the trait selection had to do with everything up to labour, not the labour itself. That's what I do in my games and it's generally worked (keeping mum green through positive needs and enhancing moodlets). Reading pregnancy books is also supposed to help increase the chance to choose traits, though I'm not sure if having the dad read them too also helps but it can't hurt!
I know what you mean about the terrible delivery pathing in IP. I played one pregnant sim who lived on a different island from the hospital and it usually took her half a day+ before she managed to get home carrying the infant - between getting there to give birth and getting home was almost a full day!
A houseboat parked nearby might do the trick, but I'm not sure if it would have to be set as the active home lot first. If your sims really need to give birth in the hospital I'd recommend a home on that island, or taking them to the hospital a couple of hours before they're ready to go into labour (that requires knowing what time of day conception happened though). If you really want to speed up hospital births you could drop a 10x10 empty residential lot as close as possible near the hospital, have the family buy it (should be about 200 simoleons), drop a tent, a fridge, and an all in one bathroom on it, and move the household there on the last day of mom's pregnancy.
Home births probably are the best way to go though. It's definitely easier to keep mom happy, she can even be placed in a room and the door locked so no other family members freak out about the labour, and there's no time delay in getting to or from the hospital. Plus she's instantly friends with the kids, which is a nice bonus.