I've seen them used but would be very leery myself. It sits right on top of the kidneys, a unbalanced bouncing child could cause pain and in turn an accident.
We've always done the same as smrobs. If there is a need to be behind the saddle it's me, I would be very uncomfortable not being able to see the child to assist if the need would arise. I pretty much do exactly as smrobs laid out and then transition to ponying them on another safe horse. My daughter is 5 and just went on her first trail ride without being ponied and by the end of our ride she insisted on being the leader :) She rides my 22 yr old retired reining mare that we jokingly say would just do radar ears if a bomb went off under her belly.
Life is like a camera. Focus on what's important, Capture the good times, Develop from the negatives and if things don't work out, Take another shot.