Hi Michele,
I've done split stays several times with my family. To be honest with you, I would keep it to 2 moves instead of 3. It actually can take a chunk out of your vacation to be dealing with packing all your toiletries and suitcases back up, working with Bell Services (transferring your bags), checking into and out of Resorts, etc.
I'm not sure if it's financially feasible for you, but if so, I would do the 3 nights at
Animal Kingdom Lodge and then do 5 nights at the
Beach Club Resort. While I've stayed in both of these Resorts, the Beach Club is one of my absolute favorites. Not only is the "Stormalong Bay" pool area amazing, the close proximity to Epcot and Hollywood Studios is hard to beat. That being said, the Animal Kingdom Lodge also offers such a unique and special experience that you'll be glad you stayed there as well.
The great thing about having so many options for Resorts is that it gives you an excuse to go back again soon to try something new ;)
Hope this helps and that you have a wonderful vacation,
Kaylene