With your vacation falling into a week before Easter, it is pretty likely that the parks will be busy/crowded. Since there are a limited number of scooters at the parks. you may want to rent yours beforehand to have the peace of mind knowing one will be available for your family member.
Scooters (or ECVs) can be reserved ahead of time through local rental companies. While I have not rented one,
The Complete Walt Disney World 2011 travel guide recommends the following companies: Apria Health Care (apria.com), Care Medical Equipment (caremedicalequipment.com), Turner Drugs (turnerdrug.com), and Walker Mobility (walkermobility.com).
All of the Disney buses & monorails are equipped to work with the scooters, so you shouldn't have any difficulty getting around.
If you'd prefer to rent through WDW, if you click
here you can find information on renting a scooter.