I have never stayed at AKL, but I have had ADRs here and utilized its transportation. Since it does bus everywhere, you will definitely notice the bus stop is very different with various sections for each destination versus Polynesian and Contemporary that only have one smaller seating area. Also, AKL and both Villas have long hallways which could pose an issue for mobility issues IMO.
Polynesian does not have the "convenience" the Contemporary does of taking an elevator downstairs to enjoy the resort amenities, however the grounds do not span very far. My mother also had two knee surgeries and has mobility issues and walking long distances can be an issue. We ultimately picked Poly to stay at since none of the longhouses are really that far from the Great Ceremonial House. As mentioned, the pools here are far superior to the Contemporary and AKL. The overall feel of the resort is extremely warm and you do feel like you are in a tropical oasis. The lobby smells fantastic and is much more inviting than the Contemporary. The transportation to Epcot is a little easier as you can walk to TTC. While it may not be right by Tuvalu, I found that making that walk was actually easier on my mother since she did not have to go down an additional monorail ramp (downhill is worse for her than up). Dining here is good, but if you dislike pineapple, teriyaki, or sushi, the menu options may get old fast. Theme park view here is further from Magic Kingdom, but a better line of sight to the castle.
The Contemporary is most convenient because of its distance to Magic Kingdom if you decide to walk. I stayed at the Grand Floridian when the monorail went down and waited 40 minutes for a boat that then had to stop at Polynesian before reaching Magic Kingdom. The whole time I was waiting I was thinking how I could have walked back and forth from the Contemporary in that amount of time. I do also enjoy the dining better at the Contemporary overall compared to the Polynesian based on types of restaurants (quick service, casual, signature, etc) and the variety they offer.
Having stayed at both the Polynesian and Contemporary, I would say Polynesian may be better given your travel party. I had also priced out both of these resorts as theme park views and personally found Polynesian to be more costly. Splitting can be a pain, especially if your new room is not ready. It can also take a huge chunk out of your day. Planning the logistics of transferring luggage, coordinating a ride since there is no resort to resort transportation and you can't bring luggage on regular Disney transportation can be hard. If price of the Polynesian theme park view is an issue, could you consider doing a few nights in a theme park view, and the rest in a Polynesian garden view room? Tuvalu has both of these rooms and garden will probably save $200 a night, easy. I feel transferring a room within the same resort may be easier to get the theme park view and save some money. Another Polynesian option could be to rent DVC points. The lake view category is limited, but all are in Moorea and have a theme park view. The first floor is a little obstructed by the Bungalows, but this could also help save on price. Just note, these studios will only have one queen bed, the queen sleeper, and murphy bed whereas the traditional rooms have two queen beds and the single sleeper couch.