The air museum is Duxford appox 60 miles 1.5hrs from London and Duxford to Silverstone is 76 miles 1.5 hours as well.
You could stop at the Holiday inn for the whole time and then fairly central for both.
The discount codes for infield passes at Silverstone are for BMW's only and you have to put the registration number of the car in when you book as it is printed on the pass so would be difficult with a hire car and booking a BMW can get very expensive.
The ticket prices for Silverstone are £110 per person for the 3 day pass.
http://www.silverstoneclassic.com/Content/Tickets
We would love to see you and travelling in the UK is ok, if we can drive in the States you can drive over here. The roads are generally busier here but just take it steady and all will be fine.
Type in (Duxford Airfield, Cambridgeshire), (Silverstone Towcester), (London Heathrow) into Google maps and you will be able to get the directions up and see how far it is.
If you could get flights to East Midlands Airport or Birmingham Airport (BHX) you would be nearer but not sure if you can get schedule flights into these airports.