Part 1:
On a naive interpretation, "recycled tub" is a health hazard.
Clean water is clean because the drain is separate from the supply.
You really really don't want sewage in the water you drink.
And if you put bath water in a potable supply pipe, you will because bath water has had someone's butt in it and pressure differentials create backflows (i.e. siphoning) in the potable water pipes.
Without an air gap, you cannot prevent it.
Part 2:
Limiting the supply would be a simple matter of adding a valve, except that a bathtub has two supplies, hot and cold.
Getting the mix right is safety critical because hot water creates a really nasty type of burn...enough that can kill a person.
Part 3:
There's a reason plumbers are licensed.
It's not greed.
It's because you didn't ask "how do I prevent backflow?"
Part 4:
Putting something connected to mains power into a bathtub is a bad idea.
It sucks if your fish die from an electrical short.
But not like if it were your child.
Part 5:
You could rig up a mechanical pump and let your child pump their own bath water to their hearts delight.
Seems like the simplest thing that would work...where working means not being a health hazard.
As a bonus a mechanical pump can be put in a suitcase and taken into a hotel room.
Part 6:
Good luck.