If you have grease in your pipes, go to Home Depot or Lowe's and pick up a can of pipe cleaner (emzines) NOT DRANO type cleaners. Put a cap full in the drain, add warm water and wait. You may have to keep adding warm water. The emzines need water to stay moist. This is the same principle used in high-rise buildings to keep all the drains moving. It works well, you just need to give it plenty of water, and a little time.
Now, if it's hair, the snake above is a useful tool. If you have something caught in it, like plastic, or something like that, then a conventional plumbers snake will do too.
The pipes in your camper are PVC, the same as most homes (except for those older ones that used galvanized pipe or steel.) So basically, any thing that works in your house will work in your camper. I caution against the caustic chemicals. Not because they will hurt your pipes, but because, if by chance you have to remove the pipes for any reason, then you have caustic chemicals to deal with too.
The emzine cleaners work well and don't hurt anything except the sludge in your pipes.
