This symptom is opposite of what you might expect. House has two showers and one gas water heater. First, if hot water at either shower is turned on all the way, you get comfortably warm water, but if any other house hot water is turned on, you get very hot water at the shower. Thus the problem, only one shower can be used at a time and no other faucets or appliances can use hot water while one is showering. What's going on?
Pure speculation ahead...
Lets say you have low water pressure or a flow restriction. Normally, when you turn on the hot water, there's plenty of excess pressure to still provide the same amount of cold water.
If turning on two hot water valves is using almost all of your pressure/flow, the pressure might not be enough to provide the same amount of cold water. If you have two hot valves open wide, and one cold valve only 1/3 open or so, the water's going to take the path of least resistance, and cold flow will reduce. In fact, pressure/flow is reduced everywhere, but is more noticeable on the cold.
So what do you do with that? Check your water pressure. Make sure the valve on your water meter is open all the way. Compare flow from different faucets and see how they compare, etc.