I have a hidden Evelynn, Entrancing at my battlefield with only a readied Stellacorn Herder equiped with Boots of Swiftness. If my Stellacorn Herder gank the other battlefield, do I have a window to play my Evelynn, Entrancing from hidden reacting to Stellacorn Herder triggered ability or does it go to the trash before ?

Yes — Stellacorn leaving doesn't trash your hidden Evelynn before you get priority, because the "When I move, draw 1" trigger is on the chain and control of a battlefield can't be lost while there's an item on the chain (Rule 187.4.c). So the order is: Stellacorn's move is instantaneous, the draw trigger goes on the chain, the state closes, and you have a window to play Evelynn from facedown with Reaction (811.6) to the battlefield she was hidden at (811.1.d.1).

Playing her there also means you keep a unit at that battlefield, so you never lose control and never trigger the cleanup that trashes hidden cards for a battlefield you don't control (323.6.a). Afterwards her play effect resolves — since it requires "a different location," her target isn't restricted to that battlefield, so you can pull an enemy unit over from the other battlefield (811.1.d.3).

One caveat: Evelynn only gains Reaction the turn after she was hidden. If you hid her this same turn, you have no Reaction, and she'd be trashed when the trigger resolves and cleanup removes her for lack of control.