Reading this thread, I am not sure if your issues has been resolved.
As an RV Tech and Montana 5th Wheeler owner, our washer drain is connected directly to the sink/shower gray tank.
Per guidance from Keystone, they required the gray tank discharge valve be open while the washer is operating. If this does not occur, water will backup into the RV via several sources, sink, washer, and shower. In the newer Montana's, the washer discharge drain-pipe is plumbed into the closest gray water tank and NOT the black water tank.
With that said, recommend contacting the RV company who installed your washer to see where they plumbed the washer discharge pipe.
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