Properly disposing of gray water is a complex task and pretty much requires the Tiny House be permanently setup.
A couple 'solutions'
What to do with Grey WaterCreate and artificial wetlandThe reality when you read the details is that unless they have an existing sewer system to hook into, most Tiny House folk just dump the water on the ground under the concept of 'watering plants'.
They consider it not sewage, but recyclable water if used to water plants.