The one in the rad is to turn the fan on.
one near the thermostat is for the gauge on the dash, and the other one is for the ECU to base its fuelling calculations on.
If you say its running poorly when cool, its not a typical coolant temp sensor issue. Normally the car will run ok cold but very poorly when warm. However, they are not much money, so its not a bad gamble to change it.
That said, pull the code for the check engine light and find out what the ecu is telling you the problem is.
Also, you can datalog the engine and read all the various sensors. If any of them are obviously out of whack, there's your culprit. IE, the coolant temp sensor reading -65 and its 20 degrees outside(before the car has started up, coolant will be the same temp as the outside air)