People make a mistake when they get a small and fragile dog as a pet for toddlers and small kids. True, they are easier for the child to handle. They are also far too easy for careless, and sometimes just plain mean acts of children. I don't have kids, but in my life, the two times my dogs have snapped at kids, they both did no harm, and the kids deserved it. (flamesuit on) But I wouldn't have pit bulls, and I wouldn't allow kids free access to pets unless they were old enough and caring enough to not corner them and poke them with a stick.
Yes, I think small dogs KNOW they are small and are less accepting of rough treatment. My runt Sheltie is the most demanding of "her" space, my over-sized guy is much more tolerant of bumps and rough-housing.