>>The reason I wanted to stay 1 night at Heathrow is our plane lands at 8pm, with getting luggage and customs I believe it would be 9pm, then an hour to London. I thought just getting something to eat then staying by the airport, wake up fresh and head to London. Maybe if I do a car service and it would drop us right at the hotel.<<

It won't be much faster getting to most LHR hotels by the time you wait for the Hoppa.

Staying at LHR is just building in a lot of extra to-ing/fro-ing and a schlepp the next morning.

Yes - a car service will drop you right at the door of your hotel . . . Or if you book a hotel close to a Piccadilly Line station (Gloucester Road, South Kensington, Green Park, Holborn, Russell Square, Kings Cross and several others) you will have a very short walk.

If you are flying in/out of LHR then it is almost certain you do not want to pick up a car there or in London . . . But you haven't told us your plans so who knows??? My guess is you'd would want to take the train up to Edinburgh, rent a car as you leave Edinburgh, and drive a bit in Scotland and down through England . . . but again. who knows . . .

Newest Plan
Fly into Heathrow take the Express Subway to Paddington Station, told only takes 15 minutes.
Not sure where we will stay for 3 nights. Believe we could take a cab to any hotel we picked.
We would take public transportation to Harry Potter Warner Bros. We would get London Passes and visit sites and hop on hop off bus.
Take the train to Edinburgh-either day train or Caledonian Sleeper (that would be a new experience).
Stay 1 night in Edinburgh-get rent a car.
Stay at Dalhousie Castle Hotel 1 night, then drive South ending back to Heathrow on the 12th to drop off the car and fly home.
Still researching what we want to see on the drive back. We like castles.
Possible stops-stay at Lumley or Walworth Castle Hotel.
See Hadrian's Wall and Stonehenge. Maybe Thornbury Castle Hotel.
With a car we can stop and see what we want. I might take a chance and not reserve a room for the some of the nights and see what I can find where we are.

>>Fly into Heathrow take the Express Subway to Paddington Station, told only takes 15 minutes.<<

You are a bit confused -- the Heathrow Express is not a 'subway' - it is a regular train. And it is ONLY helpful/fast if you are staying at Paddington. If you are staying in any other, more central part of London, then a car service will be as fast or even faster. You would have to walk to the LHR train station, then take the next train to Paddington, then take a taxi or the Tube to wherever you are staying. I'd book a car service and be done with it . . . the driver meets you as you exit arrivals and drops you at your hotel. justairports.com

(Also -- the word 'subway' means something different in the UK. There, a Subway is a pedestrian underpass. What you mean by 'subway' is called the Underground or the Tube, which is also different than the Heathrow Express train.)

>> We would get London Passes and visit sites and hop on hop off bus.<<

Both are bad ideas -- but especially the London Pass. It is VERY expensive and you have to run like mad men to get to enough sites to make it cost effective -- save your $$/££. Besides, most museums and galleries in London are free.