Brandon,
welcome to the DIS and congrats on your first of hopefully many to a great and exciting place. Wow 3 and a 4 year old - here's what I would suggest - (btw - mine are 5 and 2 so not all that far away from your's)
Do: Have an itinerary (but don't overbook/overplan) - not so, much to tackle everything at a record pace, but more so that you don't forget something you really wanted to do/see.
- At the ages of your kids I'd lean alot more towards the Magic Kingdom and MGM as parks of focus. Animal kingdom is nice, but there just isn't enough there to keep my kids (or me) interested for more than a 1/2 day. Epcot is great for slightly older kids (I'm sure some will disagree), but there are some neat things to see in Future World (Living with the Land - I think may be down for refurbishing - don't know when you are going though), The Living Seas is cool too. There are alot of educational movies and displays throughout Innoventions - and definitely take a walk thru Ice Station Cool.
As for the grownups - don't forget to utilize the baby swap option on rides that are too intense for the little ones.
In Magic Kingdom - I'd recommend (to name a few) Buzz Lightyear's Space Ranger Spin, Mickey's Toon Town, Tomorrowland Transit, Astro Orbiter, (Speedway is okay, but long lines are unavoidable)..definitely hit Peter Pan's Flight, Mickey's Philharmagic, Adventures of Pooh, (Dumbo is closed for refurb.) Ariel's Grotto is nice for photos with Ariel and sometimes Prince Eric. My DS loves Big Thunder Mountain Railroad (he's 5, but was tall enough to ride last year), the Jungle Cruise is a great ride, but Pirates of the Carib. may be a little scary for the little ones
Also don't forget to be on the lookout for characters walking thru the park - they will usually setup somewhere and families line up for autographs and photos.
As for MGM, if your kids have watched Stanley or Rolie Polie Olie, then you will NOT want to miss Playhouse Disney Live. Across the way from there is the Voyage of the Little Mermaid and if you walk to the back of that area of MGM, there is the Magic of Disney animation - look for the blue alien foot prints - they may lead you to a photo shoot with Stitch. The Fantasmic show at park closing is awesome. Again baby swap for Rock & Roll Roller Coaster and Tower of Terror.
There really is so much to do.
As for park tips and tricks - definitely have strollers for the kids, sunblock water etc. Don't try to do too much in one day you'll burn out by day 3.
Seaworld is nice (we went last year) not what I remembered from when I was a kid, but it was interesting. The roller coaster at Seaworld - Krakken is awesome. The shows seem much more educational now than years ago when it seemed the whales/dolphins were just doing tricks. It was worth the day's visit.
You didn't mention Universal at all, but I can't say from experience anything about it - we leave in 2 weeks, and will likely hit Universal for at least one day this trip - seems like there is at least a few sections of Universal that the samller kids can enjoy...I just don't know if I can handle being near some of those incredible rides and not going on them (I may sneak onto one or two when the kids fall asleep for a nap)
Anyway, wish I could tell you more, but seriously there is soooo much, I have some notes I give out to family and friends, which includes restaurant info, and it is close to 20 pages now (8 years worth of trip info and counting)
Good Luck - enjoy, have fun!