You are correct. I have no children of my own, but I was entrusted with 20 - 30 5 year olds each year for ten years. I've dealt with my share of emergency bathroom runs. Not one of them ever used a handicapped accessible bathroom.
I hope this fits your criteria of having experience with dealing with children.
As far as moving a person needing an accessible bathroom ahead of someone for whom it's a convenience....yes, I believe that should be the case.
I have also come to find your argument about a 9 month old being handicapped to be distasteful.
I truly hope you never find yourself or a loved one in the position of trying to maneuver a wheelchair into a too small space because a 9 month old wearing a diaper has a parent that feels that because of their child's age, that they are handicapped.
As far as understanding someone else's problems, try to understand the frustration of someone that has traveled across the park to the one and only bathroom for quite a while that will accommodate a wheelchair or
ECV, only to find that a mother and her perfectly able 3 year old are using it because "it's easier".