Or, if you're going with a helper, a friend, or family member, pay U-haul to install a trailer hitch on their car. That's not expensive. Then buy a trailer hitch and keep. Also cheap. When you know ahead of time that you will need the scooter, rent the small trailer from U-haul, or anyone else (like equipment rentals at Lowe's, Home Depot, etc.) and only pay a modest $30 or so for a 24-hour open trailer rental. If you worry about your scooter open, you can lock it down with a bike lock, etc. I don't think the theft rate is much for mobility scooters, so low risk anyway.
And if you have both a friend and a family member, get trailer hitches installed for both. It's a win-win, since they will be able to haul light trailers. Any car can.
On the Datsun miracle, it's possible, but you're just much, much more likely to get someone else's old workhorse, AFTER it has broken down and begins its spiral into the crusher. That's when they sell them. The fact that your family still has theirs is People's Exhibit #1.