My last two trips had some interesting configurations with kids:
Trip 1 two families: Me, my Wife, my Mom, 2.5 yo daughter, 8 month old son. My sister, my brother in law, 3 yo niece, 10 month old nephew.
Trip 2 one family: Me, my Wife, 4 yo daughter and 2 yo son.
I always plan off days into my trips, but I've always done it during swimming weather. I've never bought full ticket packages for my whole trip so all my park days have been full days. But if you can do half days at parks (go in for meals or fireworks etc.) that will help a lot too. I can't imagine having 15 mo old twins, that's a lot of work and equipment you're bringing with you! My suggestion when you start planning your days, schedule meals and breaks in to every day. Character meals for lunch or dinner, slowing down and finding a good spot for fireworks to sit down an hour before start to just relax. You'll need it.
As far as parks, it depends on what your kids are into. For me, Hollywood Studios is definitely a full day park. Magic Kingdom is a 2 day park. AK can be a full day park too. So is this a 6-7 day vacation?
Day 1: Magic Kingdom - Nearly everything in this park can be done with toddlers except the roller coaster rides.
Day 2: Hollywood Studios - If your kids are Disney Jr fans all the shows in this park are worth doing at least once. That will take a full day if you're doing the other rides and meet and greets.
Day 3: Off day / Disney Springs
Day 4: Animal Kingdom - This can be a partial day, mid morning arrival with a evening after dinner exit. Safari, shows, animal exhibits, Dino land will keep you occupied for a good 4-6 hours easily. I haven't been there in 3 years and a lot has changed, but when I went last time we did mid morning to 5pm/6pm and had dinner at the Rainforest Cafe and went back to our resort. We did all the animal exhibits, finding Nemo, meet and greets and the Safari with a few rides in Dinoland USA.
Day 5: Epcot - I'm not an Epcot expert since I never brought my kids here. I plan on doing it next year when we go. My daughter is a Frozen fanatic.
Day 6: Full day at Magic Kingdom - do everything from Day 1 again! I always love beginning the trip and ending the trip with MK. If the fireworks are too late for your children, then I would start the day later one of the days to make sure you catch them.
I don't know when you're flying in or out, but if I had 6 full days there on property, not counting travel days, that's what my trip would probably look like.