Hey, Brian! My family also likes to "resort hop" to have varied experiences, and you're going to enjoy both of your resorts.
Chip n' Dale's Campfire Sing-a-long is actually held at
Fort Wilderness Cabins and Campground, and it is free to all WDW resort guests. The Campfire is usually held nightly (around 7-8 p.m. ), and it is near the Meadow Trading Post (close to the main pool). You can bring your own supplies (for s'mores or hot dogs), but the Chuck Wagon has supplies as well as other snacks for sale. There are places to sit and places to spread out a blanket, too. A Cast Member leads the sing-a-long, and Chip n' Dale pay a visit for pictures and autographs. A Disney feature movie is shown on the large outdoor screen.
To get to Fort Wilderness, you have some options if you don't have a car available to you. From the Magic Kingdom, you can take a boat straight to Fort Wilderness. Or, if it's after park hours, you can take a bus to Downtown Disney and transfer to another bus to the Fort. Once you reach the Outpost at the Fort, you'll need to take the internal bus system to the Meadow Trading Post.
If you have the option, consider staying in ASM
before moving to
Animal Kingdom Lodge. There's a big difference in amenities when moving from a deluxe resort to a value resort, and your traveling party may be more "wowed" with each by staying in the value first. Also, go ahead and purchase at least one or two resort refillable mugs upon arrival. You'll be able to use them at both resorts. Lastly, plan your pool time or resort days for when you'll be at AKL...there is so much to do there that you can plan an entire day with tours, dining, activities, spa and pools.
Come back if you have more questions! Have a wonderful day and a magical vacation!