I built a portable plumbing unit including a variable temp shower valve using copper tubing and solder. There was a thermometer attachment used to be sold in photo stores that took a dial thermometer. All I have to do is pound a nail in the wall in the right place to hang it up, connect it to the outlets with laundry hoses, and turn it on. I had great temperature controlled water. I used ball valves for hot, cold, and tempered water. If I need to move, I undo the hoses, drain it, and put it in a box.
It looks like a strange musical instrument, but works great.
Oh yes, for a drain, I got a switch at Sears (I don't know what you would find there today) that had a switch controlled by a float. I happened to have a pump. The water drained into a five gallon plastic bucket, and when that got full the pump turned on.