As other's have said, and you seem to know, AKL is not the cheapest deluxe. WL and ALK standard are the same price. So the reasons why AKL is the "cheapest" don't apply.
AKL is a very unique resort. I don't think any resort can compare to it. But, it may not be for everyone.
We have stayed there a few times, and it's our favorite. When we stayed savannah view we always saw many animals! Last December we could only get a pool view so of course we didn't see animals from our balcony, but AKL has many viewing areas. Some viewing areas have really big rocking chairs, and telescopes to see the animals REALLY up close! The animals are already pretty up close as it is.
They have many activities for children throughout the day. You can pick up an activities schedule when you check in. Just about all the activities are free.
We always rent a car when we go to Disney.. but we also use their transportation on occasion. The busses are wonderful. Never a long wait, we never found them crowded, and because there are no stops at any other resorts.. it was pretty quick! AKL's busses were faster than the busses from the Beach Club where we stayed this summer.
For the price difference you're stating, that alone should sway you towards AKL (unless you can get the standard at WL). I really think you and your kids would LOVE AKL, so if you can't get a standard at WL.. don't think twice and book AKL.
If it turns out you can get a standard at WL, then decide if you family would enjoy a unique resort like AKL.. or a more traditional log cabin like feel (on a grand scheme) like WL.
I don't think you'd regret either choice.
Have a great time
