2001 Ford Taurus intermittent starting issues when driven distances?

I have been trying to figure this problem put all summer and have just about given up hope after having taken this to my mechanic and to ford and many other people for suggestions. When I start the car the first time of the day it always starts great but if I go distances like 30 miles and turn the car off for 15-30 minutes and go back and try to start the car sometimes it won't start up. It starts chugging usually 4 or more times and then dies. Sometimes it does manage to start after driving it that distance but it will chug 2 or 3 times and then start. Help please? I'm lost at this point and just need some good advice. I have had a lot of work done to this car and even after all of it the problems still exist.

This sounds like a symptom of a malfunctioning IAC (idle air control valve) motor and dirty throttle body. You are saying it starts but idles poorly sometimes correct? Replace the IAC and clean the throttle body.

Try the crank angle sensor.