i looked up a picture of your heater core on rock auto,the way its made you basically have a connection on each tank on the core and it does not use a divider in one of the tanks,think of a cross flow radiator and it will look similar,in your case if the core stands up in the car like the picture shows then the bottom part of the core will plug first,if it lays on its side then the lower part of the tubes in the core will plug first,you might get some improvement by back flushing the core,tho im not sure that one part heats one side and the other side heats the other side,IF you car has dual temp control so you can have different settings on each side then its most likely a blend door problem,one side of the door moving and the other side not moving,IF it has dual temp it will most likely have two motors and they will control each door separately,so it could be a motor problem,the older grand Cherokees were well known for blend door problems,a good look at a manual showing the system could tell you a LOT
im interested in what you find!!