Hi Rory,
It's the Amp Hours that give the vehicle longer to run,
If a motor is 12v, and the battery is 12 v - 35 ah, that means that the battery will deliver 12 volts for 1 hour at 35 amps OK?
If the motor draws less than this, then you get more running time from the battery, I think it's the motors amps divided into the batteries amps = the running time in hours.
I might be wrong though, but someone will put me right (usually Brian, the Electrical Engineering Genius).
I'm not well up on electricals, but I remember this from my appentice days as a mechanic.
If you get hold of larger a/h batteries, then the car will run for longer on one charge, but larger A/hours = more money! Most Mobility Scooters have 35 a/h batteries, and will go (none stop) for about 25 miles, depending on terrain and weight carried. As you children (and mine) will stop - start constantly during play, and weigh considerably less than an adult, then you should get at least a weekend out of the batteries before charging.
I can take Harvey out in his car for about 2 hours, about 1/2 a dozen times before they need charging up again.
Don't forget, that scooter and other 'Leasure' batteries, are 'Deep Cycle', and need to be run down to about 20% capacity before re-charging. Otherwise it shortens their lifespan.
Hope this has helped,
Regards,
Mark.