When my kids we small, I always flew in the afternoon. I did not want the hassle of dragging them out of bed too early and then have to deal with a cranky, tired child. It made the trip more pleasant for all parties involved!!
We take the red-eye whenever possible when we travel with our two almost 2 yr old girls because they sleep the whole way... knock on wood. We'll see if it works again in a few weeks.
I have only one recommendation .... non-stop flight.
We have flown several times with our 3 kids. They seem to do fine at all times, as long as there's not stops and layovers. For us, there's no other way we fly.
I usually fly early morning with my kids. I also bring my car seat and use it on the plane. Something about the car seat lets the youngest one(2 1/2)know that we mean business and she isn't allowed to get out ofg it. It works well for her and she's very energetic. I'll let you know how it goes after our August trip!