Car will vibrate/skip or at times wants to shut off while being idle

I have a Ford Taurus 2000.  It has about 116,000 miles on it.  My car will start fine and about 15 minutes later while sitting at a stop light/sign I can feel the car vibrate slightly.  It doesn't do it every day.  I can drive the car all day and there have been times I have come out, start the car and it vibrates roughly and I have to gas it about 3-4 times for the car to idle correctly.  Again, this does not do it daily.  I have been dealing with this since April.  I have had a tune up, all coil sensors replaced , idle control replaced, fuel pump, fuel sensor and fuel pump module driver replaced.  Recently the car overheated and the thermostat was replaced and one of the radiator fans was not working and was replaced.  There is a front pump seal leaking very slowly.  Could the transmission be the reason why I am still experiencing the problem?  Very frustrated and a lot of money spent without solving the problem.  Through the entire situation, only once has the check engine light kicked on and the code was P1237 and that is when the fuel pump driver module was replaced.  Any suggestions is appreciated,