First: Hard for me to understand that no one has sought out a gastrointestinal doctor to find out why teh constipation exists in so many. Is is a physical thing or ? (BTW, my granddaughter was found to have a too-small anus at age 1.5 months or so. The doctor waited til 3 months to do a little 6 minute operation to correct it and said it wasn't uncommon.)
Another thing: I accidentally found out that lots of magnesium makes me regular. I was taking meds that made me constipated but my blood test showed that my magnesium was low so I was prescribed it and wow, it worked better than fiber and loads of water. I'm not recommending it but I guess I'm saying that you might want to see if her magnesium is low or if magnesium supplements would hurt.
Some fruits cause regularity or diarhia in some people. Why not try those? For some, apples, grapes, dried apricots, dried prunes -- and I don't know what else.
Ask the pediatrician if you guys should see a specialist because you shouldn't live with something you don't have to.