When an engine is overheated, it is common that it will begin to miss. The engine over-temperature "idiot" light, and the fact that the engine dies, suggests a confirmation of overheating.
You ask, how could it be overheating if it it full off coolant ["antifreeze"]?
There are several possibilities as to cause [all based on lack of proper coolant flow] and the following are those that I can think of at the moment:
Again, there are probably some other causes I can't recall now.
regency
misplaced
Republic is a type of government that starts with the letter R There is also another type of government that starts with an R and that is a Regency in which the responsibilities of governing are handled by a regent who is someone other than the sovereign.
playing hooky
A part has failed. Find where the leak starts, and fix that part.
Antifreeze usually has corrosion inhibitors added to the liquid. When the antifreeze mixture has too little percentage of this (usually too much water has been added) then corrosion starts to build because of the chemical reaction of the heat, water and materials used in your radiator/reservoir.
Nobody. There are a trillion places where any river starts. What am I missing?
Tune up
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6
If the temperature gauge rises quickly when you start your car, it probably needs antifreeze. Watch out when you fill the radiator. If antifreeze starts pouring from some random place under the engine, then your freeze plugs are probably shot. Cheap part to replace -- about $5. But the labor cost ... Ouch ...
The weep hole is "an indicator of bad bearings and/or seals" in the water pump when antifreeze starts to drip or run out of it. If antifreeze is coming out the weep hole, change the water pump.