Welcome to FT!

Unfortunately, only you can answer these questions, as you know your kids. Personally, I would book the over-night flight, as their current timezone (presuming you're starting in LAX) acclimation would make it quite likely they'll sleep for a good while at the beginning, and, who knows---you might get lucky and they'll be out for most of the flight. IME, it's harder to get DS to sleep than to keep him asleep, so I try and optimize the chances he'll drift off.

As to the carseats, I would only not use them if you know that your kids will not sleep in them. IME, most kids sleep just fine---or much better---in their carseats, though, and they are safer.

It's not an easy age, though, to be sure. Good luck to you!