what happens if two showdowns are staged and I play rek'sai and I conquerer can I use the ability and play units to the 2nd battlefield where showdown will be staged and I control that battlefield

Yes — you can play the revealed unit to that second battlefield, as long as you control it at the time the trigger resolves.

When you conquer, control is established first, then Rek'Sai's (Void Burrower) "When you conquer" trigger goes on the chain (FAQ #5477). Her ability lets you play one revealed card to any valid location — your Base or any Battlefield you control — and it doesn't say "here," so the second battlefield qualifies. Playing a unit to a battlefield you already control does not apply Contested and does not start a new showdown (Rule 190.3.a.1, FAQ #5580), so the staged showdown there stays staged and will still open normally.

One thing to plan around: the staged showdown at battlefield 2 won't open until the current showdown at battlefield 1 finishes and the next Cleanup happens, so your newly played unit will be sitting there ready to participate when it does. And if your opponent's contested unit is still there, your unit's arrival means Combat is staged too, so it will open as a Combat Showdown rather than a non-combat one (Rules 323.9, 461.3).

Note this assumes the Rek'Sai legend (Void Burrower). If you meant the Rek'Sai, Swarm Queen unit, her attack trigger says "play it here," which restricts the revealed unit to her battlefield.