There are a number of companies in the Orlando area that will rent
ECVs to you for the length of your stay- you pick the number of days- and deliver them to your hotel/resort (see sticky at the top of the forum
http://www.disboards.com/showthread.php?t=595713). You would want the ECVs beginning on the 24th. Most companies rent on a 24 hour basis (e.g. 5p on the 24- 5p on the 25th is 1 day). There are generally no partial-day rentals. You do NOT need to return the
ECV every day, although you DO need to charge it nightly. You will need to have space for the ECVs in you room.
Don't be surprised if you are asked to make a deposit.
I would strongly suggest that, in addition to making a reservation, contact whatever company you choose to rent from to discuss your specific needs and your itinerary. There may some extra coordination required for service late in the day on December 24.
Many EVCs can be taken apart for transport in personal vehicles- the heaviest part for many scooters is the battery and it can weigh 20-30 pounds- some larger scooters cannot be disassembled. Disassembled, the ECV will fit in the trunk of most large cars (sometimes the seat of the ECV must be put in the back seat). Two ECVs would take up a fair amount of space.
ECVs do not need to be disassembled to use public transportation including Disney's transportation (with a few exceptions, including parking lot trams). If you are driving yourself to the parks, you should let the Cast Member directing you to park know that you have your own ECV and they will direct you to appropriate parking.
-steve