Hello and Welcome to JustAnswer. Your question is not closed until you are satisfied. I am happy to assist you with your question.
Your son could have an absorption problem, or a food intolerance, but the GI doc should be able to test for that.Has he been tested for celiac disease? As for the increasing rate of "accidents" I am more alarmed by that symptom, especially since it happens more at Dad's than at your house. Enuresis or encopresis (bowel accidents) in children who have been toilet trained can sometimes indicate trauma.
My suggestion is that you take your child to a child psychologist for an evaluation to make sure there has been no trauma and if there has been to get him the treatment he needs.