According to the rules as I read them you are absolutely correct. "the dominator chooses a single action for the creature to take on the creature’s turn" etc.
But rather than interject wonky saving throw rules and what not my preference is just to leave it to the DM and allow him or her to decide the actual details of the actions the dominated monster takes. The monster can run around the melee rather than through it, for example.
Of course, this depends on having a DM that cares about everyones fun most of all. But if you don't have that, find a new game.