Although your stated intention is the need to charge a mobility scooter, You might find other uses for a 12Vdc to 230Vac inverter, so if you do decide to get an inverter do go for a pure sine wave output model with enough power capacity to run whatever it is you are considering.
Most inverters monitor the dc input voltage and will either sound a warning or cut turn the inverter off if the voltage falls too low. This is supposed to to leave enough power in the battery to start a car, but that may depend on the car and engine size, so its best to only run an inverter when the engine is running.
I concur with Emmerson about the connection to the 12V system, the traditional cigarette lighter sockets are horrible and unreliable for long term connections. FOr units up to about 100W for longer term connections, you might consider getting an additional 7S or 13pin towing plug and using the cars towing connector, and bring the cable back into the car through the soft seal of the boot or tailgate. With power (300W and up) inverters Direct connection to the battery with short cables is best. even consider mounting the inverter in the engine compartment, and using a domestic 13A mains extension to get the power to where you want it.
Just a heads up, voltage loss along a cable is directly proportional to the current flowing in the cable. So a100W device operating at 12V dc will use about 8A of current , but at mains 230V it will use about .4A. so the losses at mains voltage are much less.