It's not main relay or else you wouldn't get it to turn over or even hear the fuel pump prime...

Alternator just charges the battery, car drives off of battery... then when battery dies, car dies, so no it's not alternator...

It's not starter, cause if it's cranking then the starter is obviously good.

I would check ignition connections, also check for a loose ground... I had a misfire problem for 2 months, and had replaced everything like you did, but in the end it was a simple loose ground that would cause the car to misfire ONLY WHEN HOT, which leads me to believe that your car has a similiar issue, as you say it doesn't start after it's used for errands (and it's up to operating temp).
Pop your hood at night and have someone else start the car, look for any sparks, that is how we found my problem...

Hope this helps, good luck!