Hi Lanning! Each Disney park including the
Animal Kingdom will offer guests the convenience to rent wheelchairs, scooters, and strollers for the day. They are not to be removed from the park.
Unfortunately, the rental location is a bit of a walk from where the buses drop you off. Since you are traveling with your family you could have one of them go on ahead and rent the chair and ask permission to bring it out to the bus area where you can then ride back into the park. I am not sure how strict they are about this but it would be worth a try.
My other suggestion is to consider renting a wheelchair for the duration of your stay from an outside vendor. You can see the list that Disney approves
HERE. Many of the resorts are quite large and your room might be a distance from the dining area and bus areas. Having a wheelchair with your 24/7 would allow you to enjoy your vacation and not tire out too fast.
If you choose to rent from an outside vendor they will drop off and pick up at your resort making it very easy for you. Add something bright such as a ribbon or scarf so you can pick it out easily and then head to the parks for a fun day.