I installed a Fisher-Pakel dishdrawer (a dishwasher that is smaller than a household dishwasher, but works the same) in our coach under the stove where the oven would normally have gone. It works great. The coach was not wired or plumbed for this modification, so I brought in a hot water line and installed a drain.
In my case, I installed a drain that would drain directly into the park's drain system rather than my grey water tank. I did that for a number of reasons and like it that way. In a pinch I could drain the waste water into a bucket or let it run out on the ground if we were boondocking where it wouldn't bother anyone. I used a one way valve to allow air to follow the waste water down the drain since it won't drain without one. The clothes washer is going to have a drain mounted high enough up to keep waste water from back flowing and still allow air to follow the waste water down the pipe. You can't block the feature. Good luck.
Holiday Rambler Navigator DP, Hummer, and Honda VT1100C Shadow