Hot water recirculating systemwith dedicated return line

So I have a new build house, and the water heater is at one end and most of the hot water demand. Such a showers in the kitchen is at the other end of the house. As you can imagine we wait a long time for hot water. My brother-in-law, who is a licensed plumber, suggested we install a recirculation pump and crossover valve to fix that problem.

Hot water recirculating systemdiagram

He didn’t explain exactly how this works-if I have a pump that’s pumping the cold water out of the hot water pipes and the crossover valve at the furthest, end of the system, doesn’t this compromise the ability to get cold water? Doesn’t this dump a bunch of hot water into the cold pipes?

Washing machine shutoffs are designed to control the water flow from the hot and cold water supply piping to the flexible hoses feeding a washing machine.

Or does it run all of the time and if that’s the case, wouldn’t all of the lines in the house basically carry hot water? It seems as if you would need a third line to act as a return to water heater to have hot water on demand as well as cold water.