Mixing valves are what you might have in a shower stall, bathtub, or sink, where you want to mix hot and cold water. Makes sense. Hence, no mixing valve at a toilet per se.
The dishwasher has a solenoid actuated valve that is either on or off. These are famous for water hammer. They are not the cause of the problem, so much as the fault of the way the plumbing is installed.
One thing you can try, to help reduce water hammer from a dishwasher is to replace the copper water supply line with a nylon one of the same outside diameter. This would be more flexible on the curve and should help reduce your water hammer.
Call a plumber and he'll save you all the hassle. And please, turn the hot water back on and take a blessed shower. phew! (GRINS)
(The plumber won't be able to trust your diagnosis and will do an inspection anyway.)