Hi Christine,
I absolutely love at stay at
Disney's Animal Kingdom Lodge,
Disney's Animal Kingdom Villas - Kidani Village, or
Disney's Animal Kingdom Villas - Jambo House. The decor is rich and amazing, and it is fabulous to be able to see exotic animals outside of nearly every window! There are so many recreation offerings right at these resorts. From African face painting to culinary tours of the restaurants, you could spend so much time exploring the resorts.
As you noted, these resorts are geographically further away from some of the Disney theme parks. They are of course the closest to Disney's Animal Kingdom Theme Park, so getting there is quick, probably about 15 minutes. Getting to Magic Kingdom Park, Epcot, or Disney's Hollywood Studios does take a bit longer. Given the ages of your little ones, I should let you know that the longest bus commute will be to Magic Kingdom Park. I would allow yourself an hour of commute time to Magic Kingdom Park, and probably 45 minutes to Epcot or Disney's Hollywood Studios. This is not all driving time, but bear in mind that you might need to wait a short while for a bus. My family has always figured that at Walt Disney World, it does not matter if it is a short ride or a long ride on the bus, it is part of the vacation and we should enjoy the ride. We often strike up conversations with other guests. In my opinion, if the theme and amenities at Disney's Animal Kingdom resorts appeal to you, I think that they are worth the longer bus rides to the theme parks.
I hope that these thoughts are helpful for you, Christine. Have a wonderful time planning your vacation, and please do not hesitate to ask if you have any further questions.