SC2Mapster

Perhaps you could give these units to player one (for team one) and give player 1 a shared control alliance. If players are concerned about someone controlling their hero, you could do the opposite of what I mentioned above. That is, if they select player 1's hero, then use the action clear selection, or deselect unit, or something like that.

The only other way via triggers I can think of is to make it so that whenever a unit is selected by a player, it switches ownership of that unit to that player. Its been inefficient whenever I've used it, as I tend to have to pick the units one by one.

Might want to ask the data forum, as there may be a good way to do it via data. I noticed there's a flag under data called "Share Control". Maybe that will help. Though I imagine you'd probably have to duplicate some units if players can have their own versions. Not really sure, as I've never used this flag before.

Adding a computer team, and giving them the alliance ally with shared control/vision/etc should work.

Probably other ways to do it as well, but this is what comes to my mind.