If your tub shower is a single handle unit most of the newer valves have a pressure balance feature. If you could post the brand name or email it to me I will explain how to check to see if this is the problem.
It turns out that the shower/tub single lever faucet (made by Kohler) has a plastic component at the base of the cartridge stem which has two holes in it that correspond with the hot/cold inlets from the pipes. Inside each of the two holes there is a screen-like mesh, I presume for filtering purposes. The mesh on the hot water side was clogged with deposits of some kind preventing an adequate flow of hot water.
We have two bathrooms upstairs. The water pressure in one is fine, however, in the other, it is really bad in the tub and shower. (sinks seem to be fine). Recently we had trouble with sediment clogging up the coil in our furnace. We’ve had that fixed and had a filter added. The rest of the house is fine. Is there a place within the plumbing of this tub/shower that could be clogged with sediment? Where do I look? Thanks for you help.