I have seen someone use a pop-up flash straight into the face of a newborn only minutes old from less than a foot away. Anyone would find that distressing, even more so a baby just arrived from the dim of the womb. Of course, those of us serious about photography wouldn't do such a thing - the resulting photo would be dreadful. If family members have point and shoot cameras with flashes that can't be turned off (or they don't know how to turn off) I ask them to avoid flashing straight into the baby's face, and concentrate on profiles.
My previous advice is for anyone photographing during labour, the actual birth, and the immediate postpartum. Once things have settled, the medical personnel have cleared out, and the initial excitement eased off a bit, then get out the MF, the tripod, the bounce flash..... whatever. It might be a couple of hours after the birth, or it might be the next day.
Once home life will be busy - grab any opportunity to take photos of the babies. I once spent 3 hours with a family with twins a few days old trying to get a photo of the 2 babies cuddled together. Didn't happen. What did happen? Diaper changes, crying, breastfeeding, repeat, repeat. It was the wrong 3 hours. I took photos, of course, but not the cuddly one the parents hoped for. That had to wait for another session. As a family member you will have more chances - if it doesn't work out one day, try another.
Quickie scan of one of my photos: