Easiest and most direct would be to take a cab. If you want to use WDW transportation, you could take the bus to Animal Kingdom Park, then bus to Animal Kingdom Villas. You could also walk or boat to DHS and take the bus to AKV.
If the Animal Kingdom Park bus is still running, I would take that bus to the park. Get off of that bus and walk over to Animal Kindgom Lodge bus. Take AKL bus to Kidani Village stop. The Animal Kingdom Park and Animal Kingdom Lodge are very close--maybe 5 minute ride.
Thank You! Is there a cab stand near Sanaa? I'm thinking of bussing there, but cabbing it back. Since at that point it will be very close to bed time for my 2 and 4 year old.
Be aware that the cab rides to/from AKL may be a bit higher than other destinations because the distance traveled is a bit further.
Depending on how late your dinner is and how tired your kids are, we enjoy taking the bus from AKL to Epcot after dinner and walking through Epcot as Illuminations happens.