Can I use one of those power converters you plug into the car to recharge the battery for my mobility scooter?

The scooter takes (2) 12V/12AH batteries and I usually plug the charger into the scooter then into a 3 prong outlet at home. Would I be able to safely plug this into a converter in my car when not in use to keep the battery charged and ready?

you can safely charge your scooter's battery using this converter, the only problem is that you cannot leave the converter connected to your car battery permanently; these converters consume electricity from the car battery, and they tend to heat alot, even when no power is consumed from the other side of the converter(the 110 or 220 vAC output), you dont wanna end with an empty car battery nor a damaged converter.

Yes, it would be safe, just make sure to unplug it after it's done so the converter doesn't overheat.

Sure, but then whats going to keep the car battery charged?

It all depends on the power ratings that your scooter needs and the ratings of the converter in your car. If the two match then you should be ok.

But before doing anything check all available documentation and talk with your scooter's user support.

It is also possible that you might be able to get a charger from the scooter manufacturer that is compatible with your car.