I think I've done this trip 30+ times by now, with kids ranging in age from 1 to 19! We have tried it every which way: no layover, short layover, long layover. My advice for kids your age:
Get it done all at once, nothing compares to the dread of having to re-board when you are feeling half dead and you have to stumble around the Frankfurt airport for 2 hours. Chances are good the kids will be asleep then anyway. Make the overall trip as short as possible.
Acknowledge that having Mom & Dad strapped into a seat next to them for 19 hours is all most kids could hope for, its way more stressful for you then for them.
Take advantage of meal times and when light are on ~ walk them around as much as you can while passengers are awake.
Ask to sit with other families
Bring the car seat but check that there is a place to store it on board if you decide not to use it. This way you'll have it when you land if your luggage goes missing.
Bring a change of clothes for the kids, and clean shirts for you. Accidents happen...
Bring their favorite snack food and decide before boarding that they can pretty much eat whatever they want.
Test drive a sleepy drug for the kids and for God's sake use it.
Don't forget to bring along a 'fun bag' as carry-on. Fill it with as many fun (quiet!) activities as you can, all of them new. New books, play-doh, pipe cleaners, sticker books. Cram it full of fun things to do and pull them out at strategic times. Spend the money, it's worth it.
If the three year old isn't used to headphones, then I'd work on that before departure
Load up an ipod with kid music and videos
Get lots of help at the other end. Someone refreshed and rested who can meet you at the airport who knows the kids is the best option.
Good luck and don't forget to take a deep breath, it'll be fine.
