I am putting in new copper piping to two full bathrooms and a kitchen. I want to use 1/2" all the way for the main hot water line to the bathrooms to limit the wait time for hot water. The kitchen is close to the water heater and I can give it its own 1/2 branch from a very short 3/4" pipe coming off the water heater. One shower is in the basement and another is on the second floor. For the second floor bathroom, it will require 50' of pipe to supply the shower. We are on a 40/60 pressure tank. Will a 1/2" main line have any trouble supplying two hot showers at once?

I was surprised to see a chart saying that 50' of 1/2" copper contains only about a half gallon. Still, if we have 2 GPM shower heads, and I'm guessing the hot water uses 2/3 of that flow, I am looking at a 23 second wait time. This seems tolerable for a shower, but not to wash your hands in the lav, which would be even longer with less flow. So, for the second floor bathroom, I'm considering adding a small electric water heater on a timer for peak demand. Is this the best way to go for my situation?

If you are repiping, I would install a return line and a recirculator. Insulate all the hot water lines. You can get a recirculator pump with a timer, an aquastat, or simply leave it on. I put my own house on an aquastat.

If you're re-piping, why not just use a gravity re-circ?