The red car can be found in the green weasel's place behind the smashed wall. It's a vehicle moving along the groove cut into the wall, which is propelled by clicking ahead of the car in the direction you want it to move.
One trail leads to a spiral with the white button in the centre. Klaymen has to press it in order to unlock the cave door.
The key Edit
After Klaymen removes the pin and unites the Neverhood, the other path, previously being a dead end, becomes accessible. It leads to the upper floor of the red Tunnel room, where one of the three keys can be collected.