I have a 95 Tahoe, there are two hoses running to the core at the firewall in the engine compartment and one other hose next to those two. It has a rubber elbow sticking out and that is where the coolant is coming from not connected to anything. I happens right after I've driven the truck and park it in the yard. If the leak is not from the core and coming from this other line, what is this third hose the coolant is coming from and how do I know for sure it's my heater core.
The heater core is leaking into the AC drip pan. That hose is the drain to let water run onto the ground. This is real common on GM trucks, especially when the coolant isn't changed regularly. Repeat failures are common due to the coolant becoming acidic.
Grab a digital voltmeter and ground one probe, and touch the other one into the coolant in the radiator. If you see a high voltage reading, flush and refill the cooling system along with replacing the heater core.