Rainbow Vale

• WWizards of the Coast2004-10-04
  Official Ruling
  Only changes controller at the end of a turn in which it was tapped for mana. It does not change controller if it is not tapped for mana.
• WWizards of the Coast2004-10-04
  Official Ruling
  Stays in the same tapped/untapped state it is in when it switches controllers.
• WWizards of the Coast2007-09-16
  Official Ruling
  The opponent is chosen when the “at end of turn” triggered ability resolves.
• WWizards of the Coast2007-09-16
  Official Ruling
  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.
• WWizards of the Coast2007-09-16
  Official Ruling
  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’.
• WWizards of the Coast2007-09-16
  Official Ruling
  If Rainbow Vale’s ability is activated during an End step, its “at the beginning of the end step” trigger won’t trigger until the End step of the next turn. If its ability is activated again during that turn, its “at the beginning of the end step” ability will trigger twice at the End step of that turn.

Rulings via Scryfall