E.D.
I HIGHLY recommend bringing a car seat on board if your child is active. There will be a tag on the seat that tells you what it is approved for (TSA approved or something of that sort). Some car seats are not approved for air travel and the airline will make you check it. My daughter (almost 3) has flown with and without a car seat. I will never do without again. She's a physical kid. Sitting, unrestrained, doesn't happen for more than 10 minutes. She will, however, sit in her car seat for at least an hour or two because she's already used to it and is actually tied in. I did not, however, bring my other child's seat (she's almost 4) because if she is focus and content, she can sit still for a very long time.
I love taking red eyes. The kids sleep, I read. I'm wiped when I get to our destination, but the kids aren't. Alternatively, I like to have a flight include nap time. That's one hour of them conked out.
Pack smart. Don't bring anything extra. It is a pain to carry around and search through. Use zip locks to separate items.
I bring: lots of snacks (but be careful not to bring fruit/veggies if your traveling from HI),
personal items,
liquid (I always bring EMPTY bottles through the security gate and then fill 'em up at the water fountain by the gate. I will not pay 3:00 for a liter of WATER.)
extra shirt for me, extra pants/shirt for them.
art supplies (washable)
two or three special toys/books and their favorite bubby, and myriad tiny toys they can role play with (ones that don't matter if they get lost). Sometimes, I'll get them each one new special something (a two dollar pony and comb, for ex.) The newness lasts the flight.
Ergo baby backpack (I have two toddlers and usually fly alone. Trying to get ID, lift bags, take tickets, etc., answer questions - I need to have hands free and brain on. I put one in the backpack and "glue" (with "magic") my eldest to my leg. That's only for checking in though.
We all wear layers. We pack our jackets in the top pocket of our bag (winter/ flying to dest. w/ different climate)
Use stroller as a cart for all your carry on items and encourage kids to get their energy out in the airport, not the airplane. Yup, I'm the guy who runs her kids through the terminal. TRUST me, you'll thank me once we're on the flight. Yes, you can check the stroller at the gate.
I do not buy food on the plane.
I DO invest in a "personal entertainment system" (ten bucks on the last plane I took). There are cartoons and movies on there. I feed my children media on a plane. It keeps them occupied and still.
If you check a carseat, most airlines will not charge you (like they do baggage). Call your airline to confirm.
Happy travels!