When Hayley triggers the portal by placing the rat skull, the skull is on both sides of the portal at the same time, i.e., it's half "ported". I think this indicates that an authorized visitor would simply tread on the exact right part of the trap as he walked in, in order to get to the "significant" dungeon.

So, maybe, plot twist - it's not that the gate is in none of the dungeons. It's effectively in all of them.

Assuming the trap is a portal of course.