When I became a parent, these dreams started. I lost many hours of potential sleep to these dreams (in addition to the expected hours lost to baby-wakes-up-and-wants-to-play/eat/cry/be changed).
My dreams usually involved the car. Usually, I'd be walking into a mall and, with a jolt of adrenaline, I would remember that my baby was still in the car. I'd try to run back but I could never get there. Sometimes, I dreamt that we were in a car accident and I couldn't get my kids out of the wreck. Who knows? That heart-pumping fear may have saved my children's lives. The dreams faded over time probably because my kids were old enough to be not so helpless if they were left in the car.
Then a year or so back, out of the blue, I had a dream that really messed me up for days. I dreamt that our whole family was walking to our car through a complicated parking structure. I was pissed because my now-almost-teenaged daughter was sassing back to show off for her friends (even though they weren't there -- go figure). I told her to wait right there while the rest of us went to get the car. She hates to be left alone. By the time we got the car, though, the parking structure was closed and we couldn't get back up to where she was. I woke up out of that one and never did get back to sleep.
The lesson I decided to take from that one was to reform my relationship with my kids because we had been getting pretty confrontational.
I realise that this doesn't address your question, eldritch, but you are not alone in having dreams like that.