I did this 2 weeks ago. My husband was with us when we flew out to our vacation, but he had to return before we did. On the way there, my boys (4 and 2) had so much fun just experiencing the flight. Your 6 year old will probably be that way. I definitely recommend taking books, toys, crayons, etc. and your 2 year olds' car seat. STRAP HIM IN! :)
On the way home, it was just me and the boys. What a nightmare. We took off at 9 pm and landed at midnight. They wouldn't wake up, and screamed all the way from the plane to the baggage claim.
But you shouldn't have that problem. I wouldn't let your 2 year old nap before the return flight (as if he'd have time with how early you have to get to the airport!), and I bet he'll sleep the whole flight.
Good luck!
Oh, by the way, getting through security can be a nightmare. Something that really helped is CROCS. We all wore Crocs or flip flops, which was very quick to get off, then back on after they went through security. We also had a backpack/leash for our 2 year old, which kept us from losing him many many times! We had to take that off to go through security, though.
You can also check to see if there are any play areas in the airport, and hopefully they'll be near your gate. We found one in Salt Lake, and one in Phoenix, which were great during our layovers.