Overheating in Summer, No FRONT heat AT ALL
 

My woes started 2 years ago, no heat. I figured a clogged heater core, so one day I decided to put a garden hose with nozzle to the heat/cold valve on the firewall...and discovered NO coolant flowing through this valve. as I crammed the nozzle on the hose fitting, IT CRUMBLED. DANGIT!

I would drive it until it began to leak, as I shoved the hose back on as best as possible...and for 2 years, NOTHING. Until a week ago...I blew a heater hose/coolant hose on the firewall...it just blew OFF, not a hole in the hose. I put it back on with a second hose clamp. 100° Texas Summer heat...well, the MAIN radiator hose blew off the next day I drove to work (15 minutes hwy driving, blew as I exited)...same thing, just blew off the radiator, wasn't destroyed.

I decided to flush the radiator and system, but remembering I have no heat and no flow, it dawned on me that there is heat in the back; lo and behold, HOT HEAT in the back seat (this would have been welcome last winter).
DOES ANYBODY HAVE A CLUE AS TO WHAT IS GOING ON HERE???
Two heater cores?

I am thinking it could simply be a thermostat for my overheating issues, but the heater core thing baffles me. The hot/cold valve not having coolant flowing through it explains why there is no heat, but how is the back heat working? Where else would there be a CLOG that is restricting coolant flow through that valve on the firewall?