I wanted to move a spouse who had been placed one generation up as being the wife of her father in law. I got the same message about not allowing a change as it would split the tree. I was concerned because I had already entered a lot of relatives to the children in the wrong generation. I went to the children of the mismatched pair and asked to move them to the real parents, being the actual father, and another profile for the actual mother shown as wife to this younger male, son of the father to whom she was mismatched. After moving the children I was pleased as I had moved two threads of people with each of two of the children, I was still not allowed to delete the misplaced mother, because her parents were attached to her. I manually transfered their information making new profiles for them on her properly placed profile and then was able to delete her misplaced profile.
Since you are moving parents who go in an up thread and moved children who go in a down thread, in each case their is a line of attached people so it seems a similar process would work for both, however in my parent situation I removed the ancestors, the grandparents, and then deleted, I do not know why i could move children and neither of us could move the parent thread. Maybe it has a special block/