Pontiac Repair: 2000 Sunfire misfiring etc, air fuel mixture, spark plug wires

Question
My car's been broken down for a while now, just brought it to mechanics today.  Started out my engine would sputter out at stop lights and while idling or in low rpm's.  The RPM gauge would bounce up and down between .5-1.0 while it sputtered, and the car would heave up and down accordingly.  On the last day it ran under these conditions I couldn't drive faster than 30mph.  Turns out I melted the catalytic converter and stuffed my muffler full of it's (the cat's) insides.  So they replaced the Cat, then the muffler, no real improvement besides the fact that it ran again with it's previous ailment.  Replaced the spark plug wires as well to no real avail, and now I'm sitting $500 poorer with no real result.  I'm told to try and drive it for another 50 miles to let the sensors and such reset and possibly straighten out the problem, but at this point it seems unlikely, and I don't want to go burning out another catalytic converter to test a theory.  I'm bringing it back to the mechanic this week to check and see if there's still a misfiring in 1 of my 4 cylinders.  Other than that, clueless as to possible problems, any ideas or solutions would be appreciated, I know nothing really about cars, but I learn concepts quickly and can investigate given enough starting clues!  Thank you in advance!

Answer
Hi
First, there is a reason for the Cat to melt down. They DO NOT just melt down for no reason. It is usually a fuel mixture problem, or Coolant.
If your #1 and #4 plugs are NOT firing or misfiring, they are essentially dumping unburned fuel into the exhaust when this happens. There could be your  problem. You MAY also have an engine mechanical problem, (faulty head gasket, weak compression, etc...) first either allowing coolant into combustion chamber (naturally coolant does not burn) or no compression the air/fuel mixture will not ignite properly.
I will say the #1 and #4 cylinders share the same coil pack.
You changed plug wires, what about plugs?
Have them check coil pack AND
I would have your mechanic check for fire at #1 and #4. Check the kv output with a spark gap tester. Should produce 40-70kv.
Have them check the coolant system, make sure it can hold pressure. The 2.2l in your vehicle are notorious Head Gasket problems (although 2000's were not as bad as earlier) they can have a problem there.
They are also hard on timing chains.
Make sure they run a compression check.
Dont spend no more money UNTIL it's fixed. You have that right. If you've already spent $500.00 and it is just the same, why spend more until it's repaired PROPERLY?
All Technicians make mistakes, I'm not slamming your mechanic. Just work something out with them.
I hope this helps.
JUST advise from experience.
Good Luck
Paul