Disney only rents wheelchairs for in the park use. You will need to go to an outside company like K&M, Scootaround or Yellow Scooters for a full time wheelchair rental that you can take to the room, off property, etc.
If you parkhop, show your receipt at Guest Relation of the next park and they'll try to accommodate you with another wheelchair without charge as long as it's on the same day. You may also want to inquire about multiple days rental, they may offer you a multiple day rate. Keep in mind that the wheelchairs cannot be taken out of the Disney parks.
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