The hot water pipe feeding the two is too small, either by build up inside the pipe (very common with steel lines), or because it was too small to begin with. Or a shutoff valve is partially closed (maybe at the hot water heater?)
The kitchen is probably closest to the water heater and the shower is the farthest. Water cools down the farther it travels through the pipes.
There may be no hot water flowing to the kitchen sink due to a problem with the water heater, a blockage in the pipes, or a malfunctioning faucet.
Stoppage
The plaming tubes are all conected.When the cold water run in kitchen the cold water at the shower become less,so with less cold water at the mix cold-hot (the balance is desterb),making the water hoter.Same if you turn on the hot in the kitchen the water will be colder in the shower.
Water is dripping from the shower head because there may be a leak in the shower head or the faucet handle is not fully turned off, causing water to continue flowing.
it may be getting air in the system .
To turn on the water in the kitchen sink, locate the faucet handle and turn it clockwise until the water starts flowing.
The shower is turned off but the water is still running because there may be a leak in the faucet or showerhead, causing water to continue flowing even when the shower is not in use.
your vent on your shower or kitchen (if you have one) is not working and either the air from the water in the shower drain is carried down stream till it T's off to your kitchen sink then the air follows to your kitchen sink drain line backwards and to your kitchen sink trap and then bubbles through your trap because your water in your kitchen trap can not drain but the air has enough pressure to go through it OR your water from your shower is flowing past your kitchen drain T and making a siphon which causes air to go through your kitchen trap and makes the gurgling sound one way to fix the problem is to add a Vent line on your kitchen drain and your shower drain with in 42" on 1 1/2 or 60" on 2" on your trap arm if you want to follow the UPC code. Note to above Respondent: That little dot next to the question mark is a "period". Try throwing one in once in a while.
More "VOLUME" flowing from the tub spout then the shower head as the shower head has a flow restrictor
The water is sitting in the shower drain and not draining properly because there may be a clog or blockage in the drain pipe preventing the water from flowing through.
The shower head temperature regulator works by adjusting the amount of hot and cold water flowing into the shower. It does this by controlling the ratio of hot and cold water in the mix, which helps maintain a consistent water temperature as desired by the user.