1997 Chrysler LHS sputters hesitates at certain speeds

Everyone is confused. ^_^ is it fuel filter, 02 sensor, leads and plugs, injectors? Engine light on all the time.
Car sputters misses during acceleration at 50 mph until I get to 60 mph.

the car idles fine at 500 rpm, but when I get to a higher speed 50 mph, upon acceleration, misses and hesitates and sputters, till I get to 60 mph. The engine light is on all the time.
The engine light flashes on and off during rapid acceleration. This is when the car hesitates sputters and looses speed runs very rough. It runs better again at a higher speed, when you are not accelerating. Driving it at city speeds it drives fine.
One garage wants to put new leads and spark plugs. Another garage wants to replace the oxgen sensor, and still another garage thinks it is the injectors. This seems like a shot gun approach which will cost me too much money in the end.
Any ideas will be greatly appreciated. ^_^
Thank you!
p.S.
the car does not start well if temp drops to freezing. I have to keep it plugged in all winter so it will start. I do not know if this is related as it has been this way since I bought the car.
The sputtering only started a few months ago.
^_^
thanks!
Darrel