We've got 3 boys, and the youngest they were when we attempted a full-force Disney(4 parks, the works) trip was ages 7, 3 and 18 months. Just take that into account as far as my experience and advice goes.
I love and agree with the advice to simply go to HAVE FUN. Take in all the sights, the little things.
Kids love parades and may or may not love characters.
Be prepared, a lot of little kids freak out at the loud sounds of fireworks. When we watch wishes, we always sit at the train station so we can make a quick exit in case one of our kids surprises us with a bad reaction.
If you can do childcare one night for a grown-up night out, go for it! It will be a wonderful time for just the two of you.
Be prepared to take breaks, and don't overdo it.
Here's my list of not-to-miss for your kids' ages:
MK
It's a Small World(always a winner with very small kids)
Dumbo
Peter Pan's Flight
Winnie the Pooh
Mickey and Minnie's House
Donald's Boat(but they will get wet)
Pooh's Playful Spot
Magic Kingdom Railroad
Dream along with Mickey show
Afternoon Parade
Cinderella's Golden Carrousel
Perhaps buy balloons for each of them, they'd love that
AK
Nemo Musical
Boneyard
Rafiki's Wildlife Express
Affection Section(but be prepared to walk, this part of the park is pretty far away)
Triceratop Spin
Character Greetings
EPCOT
Finding Nemo
Turtle Talk with Crush
Living with the Land
JIIw/Figment
DHS
Playhouse Disney Live!
Toy Story Mania
Honey I Shrunk the Kids play area
Notice I didn't put many shows in the list because kids are hard to get to sit. I would try them on Mickey's Philharmagic first and if they like it continue to other shows like the B&B stage show and Nemo stage show. HTH! Have a great trip. Take lots of pictures! I treasure the pics of my kids when they were little at the World.