You use vinegar to remove any hard water scale, as vinegar will disolve it. It is the main reason for not using tap water in cooling systems, as all manufactureres require you to use distilled water.
I have never heard of using Dawn, but I agree with Steve and would use vinegar.
Cap the bottom of the heater core and fill it with vinegar, let it sit and flush it. Do that a couple of times and you should be able to get any scale out of the heater core.
You DON'T want to pull the heater core. It is about a 6 hour job. Also, make sure that there isn't any gates or valves in the heater core lines. On some of the older Jeeps, not sure about the new ones, that had an isolation valve that opened when the heater was selected to isolate any heat sink thru the heater core in summer months. This could be stuck shut, and is eliminating the ability of the antifreeze to heat the heater core.
You should be able to wrap your hand around the heater hose when the Jeep is up to temperature to see if it is getting to the heater core. Check both lines. If one is significantly cooler than the other then it is a flow problem thru the heater core, if both are cold - then it could be the outlet at the water pump, thermostat, or the isolation valve that I was talking about before.
Let us know.