Is it possible for a child's anus or rectum to be too small and cause him to have trouble with pooping?

Yes- anal stenosis: As the intestine forms, it starts out like a long sausage that eventually forms an open space thru the middle.This gut descends to meet the skin of the outside (a different cell type) & the joining point can be tight or never actually connect. If a gloved little finger can easily enter the bottom, that is not the problem.Discuss the issue with your dr.