It very well may be how her system is...but that doesn't mean that she should be so constipated.
I have to watch my daughter closely. One missed day and we're in for trouble. That how HER system is. However, we make sure she gets the right foods each day to encourage a bowel movement daily. What goes in must come out!
First, I would steer clear of bananas. They do have a binding affect. Apple juice is good. Water is better. Make sure she stays hydrated. The sugar in juices can dehydrate them. Fruits and veggies!! I also give my daughter at least 1 yoghurt daily. Something with a live culture in it. It promotes good digestion. Quite honestly, if my daughter hasn't had her bowel movement for the day, I give her some yogurt and within 30 minutes she has had a bowel movement. But that is just her.
Stay away from a lot of starchy stuff. That binds.
Now, for the mom situation. I'm hoping you have a good relationship with your daughter in law. You really do need to talk with her. Discuss your concerns and what happens when she is at her dad's house. Let her know there IS a difference from when she first arrives to when she leaves.
Changes in bowel movements are a result from changes in diet. Our bodies react to what we eat. So, obviously she isn't getting the same things at moms. I'm not saying mom is bad. Mom may just be uninformed. Maybe she has a pediatrician that doesn't really know the full extent of the problem, or maybe the pediatrician just isn't a good pediatrician! That happens too. But it's hard for parents because we're supposed to trust our doctors and what they say.
So, it really seems like the adults in this little girls life need to get together and determine the best course of action for this child. Otherwise she is going to end up with some real problems. If it is let go, she can develop fissures around her anus, and then she will not want to go because it will hurt so bad. Then she will get impacted. That is not good.
I hope you all can work things out for your granddaughters sake.