Try this out before you laugh. If you have a child that is having trouble going poop (is it any better to say "trouble having a bowel movement"?), tell them to lean slightly forward on the toilet and layer a cuddly blanket or soft, warm towel over them. It creates a cozy tent or cocoon that provides a bit more privacy and for some reason is relaxing. All of this helps. Encourage them to relax and be comfortable, and then they can try rocking gently forward and backward to encourage the process.
Note: This works for adults too. (Again, no laughing allowed until you have tried it.)
Before you ever take over the counter medicine for this kind of ailment, always try prune juice and/ or dried fruit first. Dried apricots and dried plums (prunes) are awesome.
I hope it comes out OK. (Sorry, I couldn't resist.)