The outside of Patrick's second house appears to be a replica of Patrick's regular house. It even appears to be the same size, but instead covered in dust.
Role in episode
After Patrick hears that Sandy has arrived, Patrick uses a second rock to disguise SpongeBob with, so that Sandy will not take him to the doctor. Sandy asks him when he got two houses. to which Patrick replies he got a second one when he ran out of space to put his stuff. Sandy then asks when his house developed feet, to which Patrick replies that it is his mobile home.
SpongeBob then sneezes, causing the rock to explode and reveal its disguise.