Which hose goes to where on heater core AND motor fittings

You should be able to figure it out. It's only two hoses. Think inlet and outlet to the heater core under the dash. The inlet always comes from upper part of engine, where the coolant is the warmest and where it heats up first. The fitting will come from upper part of intake manifold or the cylinder head. then the hose goes to the firewall.
The outlet from the heater core carries coolant back to the engine and almost always to the water pump on the front of the engine. Makes sense, coolant goes back into the water pump and is circulated again back into the engine.

Follow the hoses. The one that goes to the water pump is the outlet. The other one is the inlet.

It usually doesn't matter-it just circulates coolant through the core and returns it. But the hose going to the water pump is the return hose from the core. The other hose from the cylinder head or intake manifold is where the coolant comes from and going to the heater core. Take off the hose at the water pump and you will see a stream coming out with the engine running and the heater control on hot. Try this and if the stream is not good, try swapping the hoses at the core- I mean take the hose to water pump and fit it to the core's upper hose, and the inlet hose to the lower fitting. It shouldn't matter, but let us know.

One exits the thermostat housing and the other needs to enter at a different point, usually the water pump.

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I don't know if top or bottom, but the heater core inlet will be the hose coming from either the intake manifold or a fitting on a cylinder head. The outlet from the heater core goes to the front of the engine, it goes into the water pump. I think all GM engines are like this, and almost all engine designs likewise. On a 1992 3.8L, for example, the heater core inlet hose comes from the intake manifold on the passenger side. The heater core outlet goes into a fitting on the water pump (lower front of engine).

It's just a simple small radiator. Coolant circulates through it, and the cores' fins give off heat that is picked up by the blower motor.
When the engine is at normal operating temperature, feel the two heater hoses. Both should be hot, verifying coolant is circulating through it. If only one is hot, the core may be plugged or have an air block. You can take off the core outlet hose and observe stream flow when engine is running and heater on high heat-flow should be slow but steady. The outlet hose will run from the firewall to the front of the engine into a fitting near the water pump. Some cars have a water valve in one of the hoses-make sure it is open, for coolant to circulate.

The core may be plugged, or it may have an air lock, or the core may be fine and the doors in the heater case may not be opening properly to pass heat.

With the engine at normal operating temperature, feel both the inlet and outlet core hoses at the firewall. If the coolant is circulating both hoses should be hot. If only one is hot, try cracking open the outlet line, with engine running, to get flow started from an air block. (The outlet line will run from the firewall to the front of engine near or at the water pump housing. The inlet for the heater comes off the top of engine from a head fitting and goes to the firewall.) If no flow results, the core may be plugged. To flush the core, take both hoses off at the firewall or off at where they fit on the engine, and put a garden hose into the outlet-flush it backwards-run until clear-let the water run to ground or use a catch can if able to. Some people use compressed air into the core instead of water flushing. Either way, you should see some sediment come out if it had any blockage. Once you get the heater core circulating, any further heater problems need to be addressed at the heater case. Make sure the temperature blend door can open and close-this door opens to let blower fan air pass across the heater core.
Good luck.

open hood and while looking at engine on the left side follow the lower radiator hose up to the water pump right above where the hose connects are the two hoses top goes to heater core for inside cabin the other goes to heater rail on engine their is no [bypass hose ] for water pump -on the right side of engine is the thermostat -stat outlet housing and upper hose

Heater Core Removal & Installation Front To Remove:

1. Make sure you have the anti-theft codes for the audio and the navigation system, and then write down the audio presets.
2. Disconnect the negative cable from the battery.
3. From under the hood, disconnect the heater valve cable from the heater valve. Turn the heater valve arm to the fully opened position.
4. When the engine is cool, drain the engine coolant from the radiator.
5. Disconnect the inlet heater hose and the outlet heater hose from the heater core.
6. Remove the mounting nut from the heater unit. Take care not to damage or bend the fuel lines, the brake lines, and related parts.
7. Remove the dashboard.
8. Remove the evaporator.
9. Remove the mounting bolts and remove the heater unit. Front heater unit
   
   
10. Remove the self-tapping screws and the clamp.
11. Carefully pull out the heater core so you don't bend the inlet and outlet pipes.

Front heater core

To Install:

1. Using care, install the heater core to the heater unit and secure.
2. Using care, install the heater unit and tighten mounting nuts and bolts to 7 ft-lb (10 Nm).
3. Install the evaporator.
4. Install the dashboard.
5. Connect the inlet heater hose and the outlet heater hose to the heater core.
6. Connect the heater valve cable to the heater valve.
7. Refill the cooling system with engine coolant.
8. Adjust the heater valve cable.
9. Make sure that there is no coolant leakage.
10. Make sure that there is no air leakage.
11. Connect the negative battery cable.
12. Perform the power window control unit resetting procedure.
13. Enter the anti-theft codes for the audio and the navigation system, and then enter the audio presets.

Rear To Remove:
NOTE: The rear blower motor, the rear heater core, the blower screen, the rear blower resistor (heating/air conditioning system) and the rear power transistor (climate control system), the rear air mix control motor (climate control system) , the rear mode control motor and the rear expansion valve can be replaced without removing the rear heater-A/C unit.

1. Remove the self-tapping screws and the clamp, and then remove the bolts and the rear evaporator lines with the rear expansion valve. If necessary, remove the rear expansion valve. Use a second wrench to hold the other fitting on the valve so the rear evaporator lines won't twist. Leave the first fitting loosely connected so you can use it to hold the valve while you loosen the second fitting.
2. Remove the rear heater hoses.
3. If necessary, remove the rear blower motor, the rear heater core, the blower screen, the rear blower resistor (heating/air conditioning system), the rear power transistor (climate control system), the rear air mix control motor and the rear mode control motor.
4. Remove the self-tapping screws and the lower housing.
5. Remove the self-tapping screws, and carefully separate the left upper housing from the right upper housing. Remove the rear heater core.

Rear evaporator assembly

To Install:

1. Replace the rear heater core.
2. Attach the heater hoses.
3. Make sure no air is leaking from the left upper housing and the right upper housing fitting and from the upper housings and the lower housing fitting.
4. Before reassembly, make sure that the rear air mix control linkage and door move smoothly without binding.
5. Before reassembly, make sure that the rear mode control linkage and door move smoothly without binding.
6. Reassemble the housing.
7. After reassembly, make sure the rear air mix control motor runs smoothly.
8. After reassembly, make sure the rear mode control motor runs smoothly.
9. Refill the cooling system and make sure that there is no coolant leakage.

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