My hot water pressure gets lower the further you get from the hot water heater. The tub and shower run from thr same lines and they are both down to a trickle. The double sink T's in earlier from the hot and cold water lines and runs fine. They did the remodel and tied copper lines into old galvanized lines. Can somebody give me some ideas?

Hard to tell for sure since you don't mention the age of the galvanized but it sounds pretty typical for a home built pre 1960. How was they connection between the copper and the galvanized done to prevent galvanic reaction? I would open the connection and test the volume, not the pressure , at that location. Its likely your old pipes are acting like a noose and need to come out.