NTJ. I personally find lateness extremely rude, it's like saying you don't care about the other person's time. She is not being a good friend, especially if she can't even give you a heads up if something is legitimately keeping her. But she may not realise how much her tardiness is bothering you. Put it to her straight, tell her how the lateness makes you feel, and if she blows off your feelings then just don't invite her over again.
NJH. Like yeah, it sucks, and she really had shitty reasons for not letting you in the room, but as the person giving birth the choice was hers and hers alone. I will always stand by that. But you're also not wrong for not wanting to sit in a waiting room for over 12 hours wondering what's going on, so you don't or her an apology either. However this does not sound like a healthy partnership, you two need to learn to communicate and FAST coz you have a child together now.