You can not teleport into the Tiny Hut.

While spells that restrict or block teleportation make specific reference to teleportation. Leomund's Tiny Hut restricts "Spells and Magical Effects". Is "Dimension Door" a spell or magical effect? Yes, Dimension Door is a spell. Is it being cast from outside the hut? Yes

Therefore they can not teleport into the hut. Specifically because the spell goes through it. Define through: "From one side to the other, from one end to another, in and out the other side" The dimension door goes from one side of the dome to the other side, it therefore goes through it as well as any creature passing through the dimension door would be going through it.