Taking a child to the hospital, in particular a toddler/infant, is extremely stressful. If one is already tired from caring for that child all night, I'd completely understand asking the other parent to take the child. In fact, I have done so personally, though having two children meant it also made more sense for one of us to stay home with the other child instead of towing a second (healthy) child through the hospital as well.
Also, this is an opinion/editorial piece, so whether the author watched their spouse the entire time or if the author pieced the evening together after the fact while writing this article is up for speculation.