WDW is great about providing free transportation from resorts to parks, but it isn't set up for resort-to-resort transportation. If you have your bags sent to AoA, you won't get them until 4-5pm, and it's only a guess what time they actually arrive. Your family can take an All Star Sports bus (without luggage) to AK, then AK to AoA. Visit the All Star front lobby in person and ask a CM this question about bell services. Don't call from your resort room, you'll be connected to a call center worker, not an All Star employee, and they might only be guessing at the answer. It would seem that Value resorts must offer Bell Service. Not every guest is capable of handling their bags.
I agree with PP. Take a cab, and bring your luggage with you in the cab. Pay the $15-20. If AoA has a room ready when you arrive, great. If not, AoA can store your bags until you receive notice of your room being ready. You can call for delivery to your room at that point, and it shouldn't be that long to wait.