Hot water pressure lowers when another faucet opens.

[joka8]

If I am in the shower and my wife uses the bathroom sink, the hot water in the shower will decrease until she is finished.

I had the hot water tank replace 4 years ago and this is when it started. Prior I had no problem.

 

[Redwood]

I would suspect the valve that is on the supply to the water heater to be the problem. It is probably either not open all the way or, it make be a gate valve broken in the partially closed position.