Although the road mentioned is not a divided highway, it is VERY busy with traffic. We stayed at Silver Lake, and without climbing a fence you would have to walk about 1/2 mile out of you way just to get to the road from the resort. (Quick in a car, not quick or easy on foot). Our room had a "view" of that road. Let me tell you that at shift change and opening/closing of the parks it was extremely busy. I would not have attempted the walk to AKL (closest) or AK, especially with children. Getting to the closest Disney bus stop is at least 1 -1 1/2 miles using the most direct route by foot. That doesn't consider getting through the security gates that cars/buses pass through and/or climbing fences. As mentioned, it is a hike with no sidewalks. I've never seen anyone walk at Disney because it's so spread out. And remember, you will be exhausted travelling home from the parks. The last thing to do is walk another mile. Also, AK closes earlier than the other parks, so return bus service to the Silver Lake end of WDW is slim to none after sunset.
Tednvon is right, get a car. Even at a high rate, it is totally worth the investment when you stay off-site.