On Monday, September 30, 2019 at 8:47:15 AM UTC-7, wrote:
My brother's wife wants a small water heater under the kitchen
sink. ...
There is a receptacle under the sink but it also powers the
diswasher. I am concerned that if both the dishwasher and the water
heater are on at the same time it will pop the breaker.

Breakers (thermal type) can tolerate a short-duration overcurrent, so all you really
need is a low-voltage AC relay, coil in series with... the water heater.

Problem: if it turns off the dishwasher, does the electronic controller forget that
it was in a cycle, or on a timer, and stay OFF? Old dishwasher controls (cam
and motor) would continue after interruption.

Turn it around the other way, and sense current into the dishwasher, turning off
the water heater... but the dishwasher has a complex cycle, not a constant current
at all, how would you know the right current-draw threshold?

It can be done, but running another circuit to the kitchen is easier. While you're
at it, see if 240V heaters are available, the wire won't have to be as heavy...