I would give up my child's seat for an adult, any adult, whether disabled or not, as I think it's a respectful thing to do.
I do think the behaviour of the woman was inappropriate, but some people are just always rude. I remember going out for a meal with an older woman in a group, the way she addressed the wait staff was embarassing for me, but obviuosly she was very accustomed to speaking like that to younger people.
It is worth considering that she might have been having an off day to begin with, but the pushing was just totally uncalled for.