Once you decide the approximate location for the vent, use the stud finder to determine exactly where the studs are. Now, fine tune exactly where you want the hole.
First, drill a small hole (on the inside of the camper, not all the way through the wall) big enough you can get a flashlight and take a look behind the inside panel to ensure there are no electric lines you might be cutting into. More than likely there won't be any. Once you are positive the wall is clear, go ahead and cut both sides out.
The reason you don't want to drill all the way through first is because, IF you do locate a wire, you are not compromising the outside of the camper. You can easily put a cover over the new hole and try a new hole somewhere else. Once the washing machine / dryer are in place, you will never see the cover over the failed hole.
Also, you will want to support that shelf the unit(s) sit on. I promise you, the way the screws are installed into that wall are NOT hitting studs and the weight of the washing machine and dryer could collapse that trim support. Here's how I supported mine better.
My cabinet already had 2 shelves, but under it was is the water heater. The last thing I wanted was a collapse on the water heater. So, I added upright supports on each corner that started from the floor to the bottom of those horizontal boards. I then had to do it for the next tier, and so on, until I reached the top shelf. Photos explain it better:
The original cabinet from the bedroom side:
Cabinet view from the bathroom side:
Shelves removed:
I added supports running the direction of the colored lines:
The finished result:
