We overnighted in London after our flight prior to taking the train to Dover. We usually fly Delta, so we fly into/out of Gatwick. There is a Gatwick Express train that is about 11 pounds or so per person that you take into Victoria Station in London from the airport. The trains do run from Victoria Station to Dover (sometimes you have to transfer to another station), but keep in mind that Victoria Station is large but you can surely find a porter to assist, if needed.
Here's a great link for Europe train schedules, but you'll actually find that the trains run between London and Dover more frequently than the schedule shown here: http://www.raileurope.com/us/rail/fa...ules/index.htm
. I'm really into independent travel, so I like taking the train and visiting with the locals en route, but the car or transfers may be more convenient for you all as a group. I think it's all just preference.