Think the train do a special family Gatwick deal which should keep the price for the 5 of you at around the £100 mark - can't remember exactly what they call the ticket but I think it's a gatwick flyer or something.
Also, I have booked Studio tour tickets for June and they state thaat you only have a half hour slot to get in to the tour ie if your tickets are for 2 then you have to be there before 2.30. They also say to exect queues of about half hour to actually 'check in' for the tour so to arrive early.
Is it an option to drive to Gatwick and do a parking deal for the duration or did you not want to drive after getting off the plane on your return?