I came here to say this. Even though it's mainly just during takeoff and landing when you would have to have everything stashed away, that's often when you really need something from your bags to entertain the kids (e.g. long line of planes at the runway, and kid explodes their snack/sippy cup/nose/etc all over themselves/you/the plane... baby wipes are in the diaper bag overhead).

Also, once you are allowed to bring a bag or two down from overhead, your legroom is restricted a lot more than it might be otherwise.

And then when it's time to land, you'll have to gather up all your gear and fit it back into your bags to stash overhead again. You have to do this anyway, of course, to deplane, but it's easier when it's just under the seat.

Also, I was going to mention that we have found being seated far from the lavatories preferable on flights where we anticipate our boy to sleep. That way there is less traffic going back and forth -- and you don't have to deal with one of my biggest pet peeves: the insane amount of people who think you need to SLAM the lav door shut with all your force, making as big of a racket as possible.

Good luck! Don't be too daunted by the traveling! It's just for a day (well, two with the return trip), and you can pretty much survive anything for a day. And chances are even if your kids do fuss, it will just be for part of your voyage.