I was induced for my first two, so that's no help. But, my third labor started and I didn't even realize it was labor. By the time I realized I was in labor, it was 4:30 pm. When I got to the the hospital at 7 pm, I was 8 cms dialated.
I would not have been able to bring my kids to the hospital with me. For sure, I was in too much pain!

In fact, when my DH got home at 5:30 I had him barricade me into the living room while he made childcare arrangements becuase I couldn't even stand to have them in the room with me.
But, of course, every woman is different!