My own labor and delivery was a long process - mainly uneventful, as we were induced and it took ages for the baby to agree to be coaxed out at all, but long indeed - and because we were so bored and impatient, we genuinely didn't realize (a) that and (b) why my mother was climbing the walls back at my in-laws'. The lot of them had come to visit on the evening of the first day, when we'd been in the hospital for about 13 hours and literally nothing had happened; a full day later, when she'd hardly heard a peep since saying good night the previous evening, of course she was thinking "where is that baby" but also, of course, it turns out, "what is happening to my daughter." Put a slightly different way: You're right on about the priorities but I think the importance of priority (1) can affect people other than the immediate birthing and nonbirthing parents.

I do think this particular LW's mother played it wrong, though. If she'd said she was relieved to hear her daughter-in-law was okay and she wished her son had said so sooner because she'd been terribly worried, that would have been one thing; "Why couldn't you have spared a thought for us" is something else entirely. Feh.