With the AC running, when I slow down to 20mph or less and then hit the gas (engine is right about at idle RPM), the engine doesn't respond and wants to cut-out. If I release the pedal instantly, the engine remains running and accelerates once I depress the gas pedal again if I let it roll a few more feet.

I also have a problem after a heavy rain where the car will crank but not turnover. If I crank it a couple of times and then wait for 20 minutes, it starts right up.

I've replaced the cap, rotor, wires and spark plugs a couple of months ago(expensive plugs blew the wire off) as well as the windshield washer t-connector w/relief valve just in case it was pooched and leaking fluid on the engine....but I think that the problem may be the ignition module.

Would the ignition module freaking out after heavy rain or while running the AC be causing my problems?

I have the Rex/Regina Ignition with Bosch cap & rotor.