Does player A have to appoint all 3 people below it, or can it choose to only appoint one or two?

When play A swaps, does it have to be with player B, or does it have the choice of also swapping with players C or D? Can it then immediately swap with one of the grandchildren (which would mean that you can basically put every piece in any position any day)?

After you have objects to represent all of this, how do you plan on solving it? It sounds to me like one of those problems that isn't going to be solvable with brute force.