The Dominate Person spell should make clear in its description that it can only be targeted against humanoid creatures. A player shouldn't have to wait to cast the spell to learn that, or have to resort to reading the Basic Rules.
I plan to discover, when I find an eligible target, if Dominate Person also needs to have the text from the Basic Rules about granting a new saving throw to the target each time it takes damage, what degree of control you get without devoting your action to it, and whether the spell can be resolve with a summoned object in play. None of those are specified or suggested in the game.
Like the spell in the Basic Rules, Dominate Person targets only humanoid creatures and grants a new saving throw each time that creature takes damage. The caster takes normal turns while concentrating, and the player directly controls the charmed creatures actions.
While charmed, the target is treated by other enemies as being on your team. Since the target is treated as an ally and has its own turn in the initiative order, I don't think it's going to have a problem with the caster also having a summon.
Funny log message when a dominated Orc Chieftain was killed by its orc buddies.