Here are the urls and phone numbers for off-site rentaLS:
Walker Mobility:
888-726-6837
www.walkermobility.com
Care Medical:
http://www.caremedicalequipment.com/
407-856-2273, Toll Free U.S and Canada (800) 741-2282
Randy'S Mobility is in Kissimmee
http://randysmobility.com
407-892-4777
Colonial Medical
http://www.colonialmed.com/about_cms.html
800-747-0246
ScootAround
http://www.scootaround.com
Toll-free, US and Canada 888-441-7575
I have used Walker a few times. They will ask for a credit card and charge it the day before arrival. Except for Randy's, they will deliver the
ECV to your hotel bell services before your arrival and pick it up there after your departure. Their rates, especially for longer than a week, are much better than Disney's. Also, their scooters are much better.
Your wife should be able to use a double stroller for the kids. There should not be any problems with Disney Transportation, buses, monorails or boats (except possibly boat between WL and MK).
One word of warning. Do NOT allow the children to ride on the ECV with you. They could accidentally jam the controls and cause injuries to you or other guests.