Start by ascending to the three gate switches. Have every character hold one, and use the Twins' ghost ability to keep theirs held while you proceed through the gate.
Carefully hop down the ledges to enter the maze-like mansion.
Head right and hop onto the far set of stairs reach the Twin's father. Grab the umbrella next to him.
Make your way to the top of the mansion. Use the umbrella to open the attic, allowing you to climb up. There's a Cave Painting to the left of the entrance.
Before you climb up, head down to the second lowest level of the mansion - the kitchen. Next to the dumbwaiter is a hammer. Grab this, and head back up into the attic.
On the right side of the attic is a floorboard. Hit it with the hammer to get it out of the way. Now look right to see box. Pull it back to find a fuse cell. Take it, and start pushing the box. In fact, push it as far down in the mansion as it'll go - all the way back to the kitchen.
Now enter the room just under the attic. In here, you'll find a fuse box for the cell you're carrying. Plug it in to power up the dumbwaiter, and head back to the kitchen.
Line up the box with the dumbwaiter and pull the switch. This will send it to the room where you just placed the cell.
Head up there and push the box to the left to gain access to the window. Don't go out just yet, though. Head down the kitchen (yes, again).
Use the ghost ability on the dumbwaiter switch to send yourself to the second floor. In here, you'll find a chamber pot. Pick it up, and head for the room just above the kitchen.
In here, use the pot on the faucet to get a pot of water. Now head up to the room where you can reach the window.
Hop onto the ropes outside and use them to reach the roof.
Cross the roof and pour the pot of water into the chimney to douse the fire below. Climb down to enter the room that holds the skeleton key.
With this key in hand, you can unlock the basement - just under the kitchen. Head there to find some dog food.
Pour this into the dog bowl by the front door to make the dog come to the porch. Now switch control to another party member.
Make your way to the drop-off by the gate the Twins used to get into the mansion. There's a pile of bones here, and you can pick one up. Do so and continue your descent.
As you make your way down, head right. You'll see a Cave Painting near the dog house.
When you reach the ground, keep right to enter the sewers under the mansion. Activate the valve in here to turn off some steam in the mansion basement.
Return to the basement with the Twins to reach the new area...and some rat poison. Grab this and head up the soup pot the Twins' mother is stirring in the kitchen.
With your other party member, hop up to the front door where the dog is resting. Taunt him with the bone to make him bark distract the Twins' mother. While she's looking away, switch to the Twins and pour rat poison into the soup.
Head up to the faucet in the room above a final time. You'll return to find the Twins' parents dead. You can now use the skeleton key exit through the door the Twins' father was guarding.
Make your way to the bottom level and head left. Pull the three switches to exit the level.