I think there's a slight blockage in your single drain hose. I think it would be in the last portion of the drain hose, past where the two have diverted into one hose. What I think is happening is that the water cannot drain fast enough out, and back fills back up to the shower (because it's lower than the sink drain) and then slowly drains out past what ever the blockage is after that.
1. My first attempt to clear it would be with the use of a plunger. This is easy to do if there's only 1 drain but may be different with two. I think if you can plug one of your drains (probably easier to plug the sink) and then allow water to run down the shower, using a plunger push and pull it over the shower drain. This may loosen the gunk causing the blockage and free up the pipes.
2. If this doesn't work, then I think you may have to crawl under the van, undo the clamp or T piece where the drains meet, take the drain hose off and flush it out with your gargen hose. The garden hose should fit inside your drain hose and even push the gunk out as its turned on.
I reckon you`d have it sorted with these options.