Sorry for the delay in responding. I didn't notice there were any new posts until this morning.
I'm not familiar with the 2002 Durango, but maybe there is a heater control valve or something that should normally close when A/C is selected, but yours is not closing, therefore you are getting coolant flowing through the heater core all the time.
Also, regarding the compressor now engaging after adding more R-134a - this seems like a sign that the charge is not correct. If you are able to confirm there isn't an issue with an open heater control valve or similar, it might be in your best interest to have the system evacuated and recharged. That process will check for leaks as well. Since the compressor was recently changed out, taking it back to the same shop and requesting "help" with the expense would be warranted.
-Rod