Tusks key is a key used in the Broken Home quest to open a door. It can be obtained by first entering the room that requires the doll key and then heading up the spiral stairs. After heading up the stairs you should see Tusks key lying on the floor 2 squares away from the spiral stairs.
To find the door where Tusks key is used you have to first go down the spiral stairs and exit the room that required the doll key and then taking the door to the north (beware of Ormod!). You will now find yourself in a corridor with a door to the east of the most northern wall of the corridor, enter that door. After entering the door you must then run as far east as possible in the next corridor you find yourself in and then taking the door to the south. This is the door that Tusks key opens up.