You could have a submersible pump feed a second faucet; use the tub itself as the water reservoir. This might be doable in a smaller volume than a bathtub; feed

You could have a submersible pump feed a second faucet; use the tub itself as the water reservoir. This might be doable in a smaller volume than a bathtub; feed/water trough come in 10gal to 100+ gal sizes. Plumbing wise, something much like the "garden fountain" things, just with a bigger pump and more water capacity. "powerful flow"? Really? Is it the volume of water, or is it the splash? A wider spout and/or a longer fall might make for a better display if the splash is the pleasing part. If its the impact on the pool, perhaps a narrower nozzle and more force when the stream hits the water would be better. Probably worth experimenting with. Another thought: You can probably rig this up on a activation / timer switch; so your user can slap a button and have 60sec of splash or whatever. That can be complicated with "only one activation per hour" or whatever other gates you might want to put on it.