3 week June UK Itinerary Advice Please

I would pinch a night from London to give you five nights for the Scottish section of your road trip.

Day 1-2 Bath
Day 3-4 Cotswolds - Chipping Campden
Day 5-6 N Wales - Conwy
Day 7 - Liverpool
Day 8-9 Lake District - Keswick
Day 10 Glasgow
Day 11 Fort William/Glencoe
Day 12 Skye
Day 13 Inverness
Day 14 Pitlochry
Day 15-16 Edinburgh
Day 17 York
Day 18-21 London

Read my response to an earlier query about going from Chipping Campden to Conwy:>
https://community.ricksteves.com/travel-forum/wales/north-wales-itinerary

Are you sure you want to drive the same day you arrive? Jet lag, lack of sleep, and not being familiar with the local road system can all be a problem. There are some people that are not bothered by any of those things. Others think they are ok but are really driving somewhat impaired. Still others are complete zombies and should never drive the same day. You might want to take a train to Bath and then rent a car. Don't mean to rain on your parade, just something to think about.

We are planning a four week drive tour of Wales and England and tried to avoid spending a lot of time driving. I think you have too much driving and distance factored into your plans.

I suggest spending more time in fewer places.

We are planning six nights in Chipping Camptden to visit Stratford on Avon, Oxford, Blenheim Palace, and the Cotswolds.

Also, why go directly to Bath from London and back track to see Stonehenge.

Lake District. We are doing three nights there, which gives us two full days. Think about your two nights there?

You don't seem to have much time in York. I suggest two or three days minimum.

I haven't driven in the Scottish Highlands, but I have been on tours in Scotland and I think you may find getting from one place to another more time consuming.

Thanks for the good advice. I know I'm trying to cram too much in. It's just so incredibly hard to decide what to omit. All suggestions are eagerly welcomed.
Here's a little bit about us that may help guide your advice to us. The sights of London are a high priority for both of us. My husband loves history, especially WWII history. He also loves shopping, particularly for shoes. Shopping is something I can tolerate in small doses. I love hiking and nature, and my husband likes it a lot too, probably not quite as much as I do. He also places a high priority on talking to everyone he meets, and we do meet a LOT of interesting people on our trips, as he has never met a stranger. We enjoy the art museums, although we prefer 3 dimensional works a great deal more than paintings. The UK is full of castles, but 3 is probably enough. Same for mansions/palaces. 2 is probably enough. But I have no idea which ones to choose. Any recommendations? We don't think we are interested in the changing of the guard. We've been to Hawaii multiple times and never went to a Luau. We just don't find those sorts of things interesting. I wonder what are the top 2-3 gardens in the UK? British gardens are something we have heard about our entire lives and really want to see. We make a point to see gardens everywhere we travel, even here at home in Atlanta. We will be there in June. I guess it comes back to our love of the outdoors. We have hiked the Alps on 3 different trips to Europe and find it to be the most beautiful place on earth. New Zealand runs a close second. We have hiked 26 National Parks in the US and Canada. So perhaps we will be disappointed in the Scottish Highlands, North Wales? Probably not. I expect it will be a different kind of beauty. Thanks for your help and advice. It is much appreciated.

Late reply. If you're driving to Stonehenge go via Avebury stone circle. Wiltshire is lovely. :)

https://www.nationaltrust.org.uk/avebury