You're way overthinking this. "Front hole" is simply child terminology, no more, no less.
But even for very little children (who are clearly not going to be given medical advice about a baby they are about to give birth to), it's such a ridiculously non-specific non-term.
Your front hole could just as easily be your mouth, either of your nostrils or your belly button. You might as well call your legs your 'lower arms' and your knees your 'lower-arm elbows' - or call your cheeks your 'face-arse'.
Explaining things to tiny children in a way that they can understand, but which is still simplistically factual (and not actually designed to cause them more confusion) is one thing, but anybody giving birth is going to be plenty old enough to understand basic proper terms. Not necessarily 'official' medical terms, but the commonly-understood everyday terms for each particular body part.
As PP have said, surely nobody can deliberately do something as uniquely female as getting pregnant and giving birth, all the while being triggered and offended at anybody who is there to assist them simply referring to the names of female body parts in the course of their professional services. Either the mother believes that she is a man with a vagina, ergo that "some men have vaginas" or otherwise understands that men don't have vaginas, ergo she is not a man.
Some people seem to want to buy their cake, eat their cake, still have their cake - and then make a million by selling the recipe and exclusive marketing rights to Mr Kipling.