Well, I'd think that if Superman's daughter went through labor that she'd most definitely have pain. And no, not all women tear (I speak as a former obstetrics nurse), but if the baby was coming fast and she hadn't stretched adequately to allow the baby to emerge, the doc would surely be ready to do an episiotomy that would somehow involve kryptonite. (Most everything else stretches out fine, but sometimes the introitus doesn't.)
I can also see Shayne's point that the baby could actually be hurt. I guess that would depend on the strength of the contractions (yes, some women have stronger contractions). I assume the baby would be closely monitored just as it would be with humans. If necessary, a C-section would be done. And since that would likely require kryptonite, the baby would still be in danger. I guess you'd have to decide which would be the greater risk.
Even if there was tearing, she'd heal as fast as Superman did after they pulled the kryptonite bullet out.
Yes, I'd think she'd heal quickly, too, but, of course, it would depend on the circumstances.
Interesting idea that the baby might be invulnerable while attached to the umbilical cord. It would, at the very least, surely protect the baby from those strong muscles mama has.