My car runs rough and stalls up hills?

How long since it has had a tune-up? Did this start all of a sudden, or has the problem gotten progressively worse over time?

The first suspect is spark plugs and wires. I've had a few similar models and rarely got more than 30,000 miles from a set of spark plugs. First check if any spark plug wires are loose or you can hear them arcing. Also check if the carbon string has burned away by looking into the boots on the spark plug ends. Usually when that happens, the boot will be charred and brittle around the brass terminal.

The next best suspect is carbon-tracking inside the distributor cap. That develops after moisture has found its way in there. Cleaning it is not a permanent solution. The cap and rotor should be replaced for that.

A less common problem involves the movable plate in the distributor. Your model should have an Engine Computer bolted to the air filter housing. If it does, the mechanical and vacuum advance are built into it. A different system that was also used had the two timing advance systems built into the distributor. You can identify that by the silver vacuum chamber sitting on the passenger side of the distributor, just below the cap. It will have a small black rubber vacuum hose attached to it. That vacuum assembly pulls on a movable plate, and that causes repeated flexing of the wires for the magnetic pickup coil. Over time that flexing can break the two wires resulting in anything from a crank / no-start condition to intermittent stalling when the engine is warm, to intermittent backfiring.

One way to check for broken sensor wires is to disconnect that vacuum hose at the distributor, plug that end, then drive the car to see if the performance changes. If the symptoms go away, suspect that pickup coil, but don't continue to run the engine that way. That resulting loss of timing advance will destroy your fuel mileage.

Another test is to disconnect that same hose, but from the other end, and momentarily touch it to some other vacuum source. We can work on that later if it appears to be a test of value. That will exercise the movable plate while the engine is idling. If symptoms develop or change while doing that, it is another sign those wires are coming apart on the pickup coil.

A plugged catalytic converter can also cause backfiring, however, the engine will run unusually smoothly. The additional clue is the sound at the tail pipe will be a steady hissing noise instead of the characteristic "putt putt". Catalytic converter problems can develop too from misfiring spark plugs. Those send unburned gas into the exhaust system where it will burn in the converter causing it to overheat and melt the catalyst. That melting blocks the free flow of exhaust gas which leads to the backfiring. This is a case of where there can be two different problems. Both the spark plugs and the catalytic converter must be addressed at the same time.

That last thing to consider is a plugged pickup screen, or "sock" inside the gas tank. I've had two of those on my carbureted cars and twice on my fuel-injected '88 Grand Caravan. The symptoms are completely different between the two fuel systems. On your car a plugged screen acts like the typical running-out-of-gas problem. That screen is not to be confused with the fuel filter down by the fuel pump at the right front corner of the engine. On Chrysler products those fuel filters typically last the life of the car. I wouldn't tell you to not replace it, but it would be a first for me if that is what solves this problem. The common symptom for a plugged or collapsing screen is the engine will run fine for about 15 miles, then you'll lose power and soon be sitting on the side of the road. After sitting for a few minutes, the screen will stretch out and allow fuel to pass, then you can restart the engine and drive for another three or four miles.

Let me know if this helps or if you have any other symptoms or observations.