Accommodations at WDW that include a kitchenette will largely be DVC villas -- which come as studios, 1-bedroom, 2-bedroom and some 3-bedroom. While mostly offered as Vacation Club accommodations, you can book these with cash through Disney directly. DVC points can be rented, either from an owner or through a 3rd party, but be aware of cancellation terms if you go this route.
Depending on the kitchenette needs, the Family Suites at either All Star Music or Art of Animation all have basic kitchenettes. One other option may be the Cabins at Fort Wilderness, though that isn't a typical "resort" and may or may not suit your needs but they do have a full kitchen.
All resorts have rooms with a roll-in shower. Make sure you check the "Accessible Rooms" checkbox when searching online. The description will specifically state "wheelchair accessible with roll-in shower" -- be aware there are different types of accessible rooms, some have tubs, some are not wheelchair accessible but hearing accessible, etc. So watch the descriptions.
A lot of which level of resort you choose will depend on budget. DVC villas are considered "deluxe" level resorts with higher price tags. Art of Animation and All Start Music are "value" level resorts with lower price tags.