Your plan sounds good. Just make sure you stop enough and get them out of their car seats to get pressure off their legs - once in a while there's a child on the news with nerve damage from a long drive from not stopping enough (usually a kid in diapers.)
I would get the kind of ticket that #1, will let you in early before the general crowd. #2 - I would not get the option to hop parks within the day because it's hard on the kids and it costs extra (unless that's the only way to get option #1.)
The earlier you can get in, the better. Feed the kids breakfast in your room rather than buying at Disney - food is SO expensive there, even a carton of milk! I would not buy their meal tickets. It's not worth it. There is a super Walmart nearby where you can buy stuff to make sandwiches and fruit as well as the breakfast stuff. Put together sandwiches and all that and put water bottles in the little freezer the night before. Put your soft insulated bag with the frozen water bottles and sandwiches on your umbrella stroller and that will take care of water and lunch. (The park water in the fountains tastes terrible!) In the heat of the afternoon around 2:00 or even earlier, go back to the room and put them down for naps. After they wake, maybe that would be a good time to use the hotel pool. Then go back to the park, and eat dinner there. Get back to the room by 8:00 for bath and bed.
Animal Kingdom is HARD for little kids. The terrain is hard for strollers - I was actually in a wheelchair there after surgery and I couldn't walk any of the parks for long, and if I couldn't have walked some, I would have had to just sit and wait for everyone. The open humvee type vehicles for going on the "safari" are very jarring. Thank GOD I had a donut with me to sit on, or I would have been in a lot of trouble (I had stitches "down there" and didn't realize how much my butt would be going up and down on that vehicle's seats!) So think about that for your kids. (You know your kids - I don't.)
Take a bag of dry clothes and ponchos that fit them. It rains a lot for short periods of time. (Ponchos for you too!) There is a place that little kids love, love, love that has water that shoots up out of holes. My sons were SO happy that they spent more time than I care to say letting water squirt in their faces, and my younger son was still in diapers. His diaper was so full of water that it nearly hung on the ground! LOL! I took off his clothes so that they wouldn't get wet, but according to when you go, if it isn't real hot, you might want to leave clothes on him so he won't get too chilled.
Take small toys or lovey's and little books to enjoy in the lines. Make use of the option of getting a later ticket to a ride to go through the express line. And it's okay to go through the same ride over and over, like It's A Small World and Buzz Lightyear, if YOU can stand it!
Have a wonderful time! My boys STILL love Disney and they are older teens.
Dawn