The rules for Secret Passage in the Battlegrounds Domination rule book state:
As a move action, a creature in a zone with a Secret Passage may move directly to another zone with a Secret Passage. This creature ignores intervening walls and zones during this move.
Pushes and Teleport are not move actions, so no, -a creature can't be pushed through a Secret Passage.
I'm not as sure about Blue Gremlin. If a Blue Gremlin were Tanglevine'd in a zone with a Secret Passage, its Mage could pay 1 mana to make its move actions into Teleports to an adjacent zone... which could break it out of the Tanglevine but I'm not sure if that same move action could take it through the Secret Passage. But that's a relatively unusual situation (e.g. Why would anyone Tanglevine a Blue Gremlin?).