3 days to drive from Heathrow to Scotland

It sounds like you are actually counting on 4 days -- day of arrival plus 3, is that right? If you have only 3 days total to travel from LHR to Inverness, then I think you need to forgo either Cotswolds or Lake District or Edinburgh -- in other words, see two out of three of these destinations.

It's really best not to drive while jetlagged, but the Cotswolds is not very accessible by public transportation. This company appears to run shuttle service between LHR and Cotswolds towns. https://witneyshuttle.com/cotswolds-airport-shuttle/ If you stay in Moreton-in-Marsh I believe there's car rental there so you could pick up your rental car on the morning of Day 2. This thread gives other suggestions for how to use public transport to get to the Cotswolds from LHR. https://community.ricksteves.com/travel-forum/england/transportation-to-cotswolds-from-heathrow

The Cotswolds leaves you still an awful lot of ground to cover in making your way north to Inverness in just 2 more days. Are you sure you wouldn't be just as happy taking the train from London to York on Day 1, then Edinburgh on Day 2, and Inverness on Day 3?

If you're really determined to see the Cotswolds and to rent a car, then Day 2 will require either a long drive to Edinburgh or a moderate drive to the Lake District. As noted above, I suggest you limit yourselves to one or the other. From Lake District to Inverness is a very long drive; from Edinburgh still long but not as bad.

The advantage of these long-distance drives is you'll be on the Motorways, where people tend to drive really fast (of course all drivers should observe the legal speed limits, but in practice many don't). Note that the rule of the road is to use the inside (right) lane for passing /overtaking only; it's not like a U.S. freeway where you choose your lane and pretty much stay in it. I'm told you can actually be ticketed for hogging the inside lane.

Driving straight off a flight, followed by another long day of driving really isn’t a good idea! Plus three one night stops will be tiring and you will be spending longer staring at tar roads than out seeing places.

If you arrive early in the day, you could take the train to York or Durham, possibly hiring a car to get out and see some rural life, not just cities. You could then either continue to Inverness by car (7 hours drive from York) or better, hop back on the train. You will be more refreshed and this will be less driving, as the countryside is better the further north you head. From York you could see the Yorkshire Dales or the North York Moors. Towns such as Pickering, Whitby and Harrogate are all worth visiting.

From Durham, you can cover Hadrian’s Wall and rural parts of County Durham. Beamish Museum is a whole day out.

We did a four week drive tour of Wales and England last October. Here is the link:
28 days in Britain and Celebrity Eclipse home
https://www.cruisecritic.com/memberreviews/memberreview.cfm?EntryID=599139

We spend six nights in the Cotswolds and used Chipping Campden as our base. Also, we visited the Lake District (Keswick) and spent three nights there.

1) Each person has to make their own determination if they can drive safely after a transatlantic flight. I did so and had no problems. We drove to Bath from Heathrow.

2) Your plan to spend three days in route to Edinburgh is basically a drive by. You will see some of the countryside, which is awesome, without savoring the many sights to see there. We spent six nights in Chipping Campden and did day trips to Oxford, Blenheim Palace, Stratford Upon Avon as well as all the wonderful towns and cities of the Cotswolds. Rick Steves one day Cotswolds drive, stopping in each place took us a day a half/ The Lake District is awesome, but just driving through there will give you only the tip of the iceberg.

) I have another suggestion, avoid the monster drive that you propose. Traffic in Britain, even in the North of England is never easy and if Mapquest says a route is 2 hours, plan on 3 or more, especially in the South of England. The British countryside is wonderful, but to see it well, you need to take side roads with either those stone walls or hedges bordering the road, instead of the interstate like highways. However, you will be going through towns every 5-10 miles having to slow down to 30 MPH. Beware, those little towns have speed cameras and I got a 40 pound ticket for going 35 MPH in a 30 zone. I recommend taking the train from London to York. We spent three nights there. It was amazing. The minister is awesome and the ancient walls can be walked. Don't miss the National Railway Museum. Spend at least two nights there and savor the sights you see. Don't miss most of the iceberg.

Thank you so much for your suggestions. You have confirmed my concerns. If I went strictly by the google maps times my original plan might not be too bad, but knowing that those times don't take into account reality, I need a new plan. I will look into your York ideas. I visited years ago so it would be good to go back. I also had considered Yorkshire Dales. We've never been there so that's a great option.

Yes, that’s lot of driving, but if you don’t mind it, it’s doeable. Heathrow to the Cotswolds is about a 2.5 hours drive. You could visit (suggestions only) Burton on the Water and Stow on Wold for short stops (gets you out from behind the wheel) then spend the night at Stratford Upon Avon. From experience, by the time you reach Stratford you’ll know it’s time to get off the road. The next day drive up to Keswick/Lake district. Since that drive is all motorway, it should be an easy drive. I wouldn’t want to drive in Edinburgh, so maybe find a place outside of the downtown area and take a bus to see the sights.

We certainly don't mind driving...prefer to mix in some scenic routes with motorway. The more I look at options the more I realize I have my heart set on Cotswolds. I wonder if we would enjoy Thursday and Friday exploring the Cotswolds, get up early Saturday and take the M5/6 to A7 to Edinburgh. That would put us in Edinburgh late afternoon. We would overnight there and leave mid-day on Sunday for our house near Inverness. I've been to Edinburgh before so less than 24 hours there won't be a problem. Does anyone have any good suggestions for a few short scenic detours to do on the long drive to Edinburgh? It looks like we'll be going through the Lake District. Is there an easy place to stop and enjoy some scenery/quaint towns, etc? I really don't know anything about this area. OR, any suggestions for alternatives to Edinburgh? We could stick to the western side of Scotland, but I don't know anything about that area either.

Keswick is right on Lake Derwent Water. There are water taxis that will drop you off at different places around the lake, or you can walk part way around the lake and take the water taxi back. On the way into Edinburgh you could stop at Rosslyn Chapel (seen in the DaVinci Code and linked to the knights templars and Sinclair family). There are a number of Woolen Mills in the area around Peebles if you like woolen goods.

Thank you! That's very helpful.

Consider landing at Heathrow and then go to London Kings Cross station for train to York. Stay in York for a night or 2 and then train to Edinburgh - stay over. Then train from Edinburgh to Inverness (or hire a car for this leg).
Pre book these longer train journeys about 11 weeks ahead to get the cheapest prices - on specific trains. SEE >
www.nationalrail.co.uk
First train will be KGX > YRK.
https://www.visityork.org/?AskRedirect=true
http://edinburgh.org/discover/itineraries/two-day/

" You have confirmed my concerns. If I went strictly by the google maps times my original plan might not be too bad, but knowing that those times don't take into account reality, "

I would always recommend using the AA route planner rather than Google Maps:
http://www.theaa.com/route-planner/index.jsp

Sounds like you are travelling from USA?
Another option is to fly directly into Manchester then from there up to Lake District or across to York

You guessed it...traveling from Atlanta! That’s a great idea, and one I had not considered. I just checked flights, and it’s only a few dollars more to fly directly to Manchester. I think that’s the way to go. Now the question is: one night York, one night Lake District, and one night Edinburgh OR just Lake District and Edinburgh? Since we are going to be in the Scottish Highlands the next week, should I skip Lake District? Will that be similar to our Highlands experience?