How can you fix plumbing when the upstairs hot water in the shower turns off when the taps or shower downstairs are running?
Not knowing the age/size/configuration of your plumbing or it's condition, I can only suggest what might be causes for your situation.
. Your pipes are old and the interior of the pipes have become narrowed by rust or corrosion.(over time sediments collect on the interior of your pipes and severely restrict the flow(volume). The older the plumbing the more chance this has happened)
. Your water supply pressure is too low. . A restiction in the shower head/diverter. . Corroded valves in the shower.(not fully opening) . Supply lines are to small to handle all the fixtures at one time. . Main supply line valve not open all the way. There is a multitude of things that could cause this situation.
.Taking off the showerhead. Turn on the valves, hot and cold, test one at a time, and see it there is sufficient water coming to the shower when the valves(upstairs and downstairs) are both open. This will identify if there is enough water coming up to the shower and if it is just in one side.(hot or cold)
If there is sufficient water flow: Clean or replace the shower head.
If not: . Check the sink/toilet water flow and see if they slow or stop running when the downstairs shower is running. If they too slow considerably, it is probably a problem common to the supply line to the upstairs. . Check your water lines(hot or cold) feeding the upstairs shower to see if it is large enough and tied into a line large enough to carry the demand.
You can also:
. Test the water pressure as near to the Main suppy line as possible.(outside hose bib) You can get a gauge to screw onto a hose nozzle for a few dollars at the hardware store.
Unless you have a Water Pressure regulator in line with the Main Valve, the water pressure should be the same at all outlets.
If you do have a regulator, the "presuure"(not volume) may be reduced after the Regulator but shold still be at a new equal pressure throughout the house. note:(Water Pressure Regulators help protect your fixtures from excessive pressure and surges. High pressure could cause leaks or failure of some units.)
The gauge may help you identify where a restriction may be located.
If the upstairs shower was added during a remodel, it's possible the supply lines were not properly designed to handle the extra water demand. This would require some plumbing renovation to bring it up to specs.
As a general note: Old 3/4" galvanized pipes after time can restrict down to pencil size or smaller inside. Even plug off completely. You know what that will mean...