It appears that we will have to take the express from Gatwick to London, then get to Charing Cross station to get the train to Canterbury. Is it feasible to simply rent a car at Gatwick and drive the 52 miles to Canterbury? Seems like it would be a timesaver. Then perhaps return the car to a lot very near a tube station when we return to London, where we could just take the tube to our London hotel. Any suggestions or feedback on this? Our timetable is Sept 11 -13, 2010. Thanks.
If you decide to go by train it will be quicker and more convenient (maybe a bit more expensive) to get the First Capital Connect service from Gatwick to St Pancras and then the domestic high speed train from St Pancras to Canterbury.
It's certainly feasible to drive from Gatwick over to Canterbury. Going by rail would almost certainly involve going into London to change trains.
As to where to return the car, I'd suggest doing that well clear of the London area, which means outside Tube range. There are any number of towns between Canterbury and London where you might return the car, depending on who you rent if from. For that matter, it would be just as easy to return it in Canterbury and grab a train there. If it was me, that's what I'd do.