My tub/shower has a single handed control to turn the water on and adjust the temp. It points down when in the off position. To turn on you must go counter clockwise then to access hot water you must continue further counter clockwise to get the water hotter. When I turn the water on the cold water comes out fine. However, as I continue going further to get the water warmer water stops flowing and shut slate down then when turning it off and goes back to blue (cold) the water starts flowing out again and then shuts down. So the water shuts down when trying to get it hot and the water never get warm. The closest sink next to that tub seems to have that the same issue. All other showers and sinks work well. Has anybody ever encountered this? By the way both off these are also the least used in the house.

yours sounded like a very common problem until you threw the one sink into the equation.
now it makes no sense to me..

It appears that your single handle mixer has a cartridge has failed and should be replaced, with a new one.
Best Wishes