I honestly don't care if mom carries the child to and fro. Maybe it's because my own kids are now a bit older and I'm realizing just how quickly the time goes.
BUT, I draw a line at being expected to continue that carrying/babying. I have a mom who tries to hand off her very large 3 yo child to me each morning. I told her, my back can't take that, you can go out him in the cozy spot until he's ready to join the group.
This job can be so hard on a providers body that I do try to minimize the carrying, lifiting, up and down etc business.