Rainbow Vale

The opponent is chosen when the “at end of turn” triggered ability resolves.

If control of Rainbow Vale has somehow changed before the “at end of turn” ability resolves, the player who activated the mana ability (not the current controller of Rainbow Vale) chooses one of their opponents to gain control of it.

If more than one player manages to tap it for mana in a given turn, then two control-change abilities will trigger at end of the turn. These abilities resolve using the standard order for such things, so the active player’s triggers are put on the stack first, then the opponents’.