The urge to go with uc is often a small amount of material (or gas) hitting an inflammed area. As a fully potty trained adult (I think!) with uc, I often cannot tell the difference between a full bowel movement, a small bowel movement, an unproductive bowel movement, or gas. Many times it's all the same feeling.
I sometimes feel frustrated when I rush to the john only to find out I've dropped trou for gas. I imagine rushing a child to the toilet and disassembling a diaper and all that jazz is at least equally frustrating for you, but that's probably a part of potty training a child with uc. I don't envy you.