engine light on after putting in more coolant

Adding refrigerant alone can't cause the check engine light to come on. You'll need to get the code read and report back to give some kind of direction. Was the car only blowing warm air, then after the refrigerant was added, was the A/C blowing cold again? Not enough info from description given.

There is not a single code that can be caused by the air conditioning and refrigerant system that affects a check engine light. We're talking apples and oranges here. Have testing done that makes sense and stop guessing.

It sounds like you had FREON for your A/C system put in and your having a COOLANT/ANTIFREEZE issue if the vehicle itself is running hot. Your A/C system will also not work if your vehicle is overheating. The "stumble" feeling may be the car bucking from the overheat. Agree with Dave don't guess you may actually be hurting the engine. Overheating can cause costly repairs. Have it looked at. May not want to drive it depending on how quickly it overheats. Hope this saves you some dough.