Just installed new electric water heater. Water is lukewarm to all sinks and showers until I turn on the main bath shower, which somehow allows hot water to be available at all the sinks. Was thinking the main bath shower control is allowing cold water to mix in with the hot and allow it to pass to the other fixtures. Is this possible.

Yes, actually somewhat common. If your shower faucet is a single handle controlled faucet, then I would suggest replacing the cartridge and see if that cures your problem.