Great Britain Trip - WHERE to start?

I would start your itinerary in London, and follow the order in which you listed your areas of interest.
"London (4 days) Portsmouth (1) Bath (2) Conwy/Snowdonia (3) York (2) Durham (2) Edinburgh (2) Stirling (1) Scottish Highlands (4). I don't care where I fly into or out of. In rough terms, I see the trip in 3 parts - London & Southern England / Wales & Northern England / Scotland."

You wrote,
"To my mind I would organize my itinerary in the order I listed above - fly into London, out of Edinburgh or Glasgow. Is there any reason I should NOT do this?"
No, there is no reason you should not do this. That is the ideal way to do your flights.

You also wrote,
"I figure that London will be just as good to get over jet lag as anyplace (although RS recommends Bath) and doing London last - this seems like unnecessary travel (although I understand I return LHR ticket is likely the reason)."

London is, indeed, as good a place as any, to get over jet lag. About the RS recommendation to get over jet lag in Bath, it is not etched in stone just because he suggested it in his book or tape. Jet lag should only last for 24 hours. The best thing to do is to drop your bags at your hotel and take a walk when you get to London. Walk along the river, take a river boat ride (Thames Clipper is the best.). When you start feeling like you can't fight off sleepiness any longer, get some dinner, go back to your hotel, and turn in for the night, even if that puts you in bed at 7:00 PM.

Going to bed early is a good way to get all the sleep you need and to be ready to go in the morning. This is what my husband and I did when we went to England for three weeks in May 2016. Early to bed, no jet lag problems the next day.

Train service is good in southern England. You will have no trouble getting from London to Portsmouth, or from Portsmouth to Bath by train. On the way, you will pass close to Salisbury, a town with a great cathedral (houses one copy of the Magna Carta) and Stonehenge nearby.

You will have no trouble getting to Conwy from Bath by train. All your places on your itinerary are easily reached by train, until you get to the Scottish Highlands. Then you will need a car, as I am sure you already know.

Sorry, I can't help you on your question about attending a Highland Games. I have never been to one. Maybe someone else will chime in later with that information.

I have been watching your question all day, and was waiting to see if three or four others would jump in and comment. As no one else has, I will blab on.

About London. You asked "Is there a reason I should avoid London the last week of August?"
No. The only "big" activity that I can think of in the last week of August is the Notting Hill Carnival. It is somewhat-- not exactly--like Mardi Gras in New Orleans. There is also a pickpocket element that goes with the huge crowds that gather on the streets of Notting Hill, to drink, party, and watch the gawdy parade.
This is an event I would avoid. But it is confined to a specific area. You will not come across it if you are around the regular tourist attractions.

The only impact that the Bank Holiday will have is that London and other touristy places, (such as most of the places on your list!) will be busier and therefore more expensive. The other possible impact is that the rail network maybe closed in some places to allow engineering work to take place over the long weekend - it's too early to say if this will be an issue. Most things stay open over the Bank Holiday, but local shops in smaller towns and villages will be closed on the Monday - this isn't likely to affect you.

It's up to you to decide if you want to cover London, but if your children have never been, it seems a pity not to give them a taster. Don't start your trip in Edinburgh, as it will be Festival time, hideously busy and very expensive, so cover this in September.

Only visit Portsmouth if you are into naval history - the town itself is dreadful. Likewise, only getting half a day in Bath after travelling is a waste, as you won't have enough time to see much and it's quite out of the way. Consider scrapping Portsmouth and adding this night to Bath. Four nights in the Scottish Highlands isn't very long, as this is one of your favourite areas. If you are going to Skye, you need three days on the island to start to scratch the surface I would scrap Portsmouth and Bath and add these to the Highlands.

Wherever you land, please don't hire a car immediately on arrival after a long flight!

Rebecca - Thank You! for all of your replies. Great suggestions. Thanks for the confirmations of my rambling thoughts. Cutting back on London is something I will look harder into so I can add that to the Highlands. Good jet lag ideas - I have always found having a plan to deal with that gives the best results.

Jennifer - I think you have confirmed my idea of starting in London. The Bank Holiday will like affect the big city less than smaller ones. You are right about London - my kids have never been and there is too much there to fully skip. Definitely not starting in Edinburgh - want to avoid the festival, thanks for the reminder. I LOVE naval history. We went to Portsmouth on our previous trip. But not sure if the rest of the family will be as keen on going, I may have to skip it on this trip and as you say, add that to the Highlands. Just too much to see!

Thanks for your thoughts. Now onto serious itinerary planning...

In London there's the National Maritime Museum, which might satisfy your interest in naval history without taking the time to go to Portsmouth.

One of the best sights in London for kids, teens, or adults, in my opinion, is the Tower of London. Kids of any age love the castle-like appearance, the bloody history of the beheadings, and listening to the Beefeaters' give their tour! Get to the Tower first thing to start your day, to avoid the crowds that get there later. The Tower of London has a great lunch room/cafe where we ate lunch. A good selection of sandwiches, salads, main dishes, such as chicken and dressing, also good desserts, coffee, tea, Coke, Sprite, and fruit drinks.

After visiting the Tower, the next thing to do is to step onto the pier right there at the Tower. Take the Thames Clipper boat to Greenwich. This will give you a great ride on the river, and a look at some of the landmarks from the river. The boat will go under Tower Bridge. At Greenwich, you can tour the Cutty Sark, a huge old tall masted sailing ship. Really cool and fun. Also visit the Maritime Museum (free) and walk up the hill to the Greenwich Observatory. The view back towards London down the river is beautiful.

The British Museum is probably someplace you and your wife went to in 2004, so you've probably seen it. But I think it is also a great place for kids. There's something for everyone there. Their cafes are very good, and they serve a very good afternoon tea with sandwiches and sweet cakes, if you guys are ready for a break then.

The Victoria and Albert Museum is also great. Something for everyone. Paintings, silver goblets, Tudor and other kinds of jewelry, costumes, medieval tapestries. Also has a good cafe with sandwiches, salads, and desserts.

I would also consider a day trip out to Windsor Castle. It's amazing, and I think the kids would love it.

A good way to get a quick view around London is to take one of the Hop-On-Hop-Off bus tours. One of the companies that does it best is the Original Tour. They go by all the "must see" sights of London. And you can hop off anytime you want, look around a sight, then get back on the next hop-on bus that comes by. The tickets are good for 24 hours.
https://www.theoriginaltour.com/p/tickets/the-original-tour/
https://www.theoriginaltour.com/#n
Notice this on their home page:
"All tickets include 3 FREE Walking Tours, a FREE Thames River Cruise Pass, FREE Kid's Club and unlimited access to all our bus tour routes."
There are several different routes. You can go on all of them for the ticket you buy. Be sure to go on all the routes, so you see everything and get your moneys' worth.
Route map:
https://www.theoriginaltour.com/media/1884/the-original-tour-map-hr.jpg

I would use the hop-on-hop-off bus as a way to give you a tour around the city, but regular red double-decker buses are the way to go for just traveling around London every day. In addition to the tube, that is.

That's just a start....there's so much to see in London! Hope this helps!

Rebecca - again, excellent suggestions. Thank you!

Wow, Rebecca!! Excellent!

I will just add a few points.

-I would definitely keep London in the mix with the kids just because...it's London! I don't know if you have lived where there is public transport but if not this is a terrific way to introduce them to that. I think it is good to have kids see and identify with iconic sights - you know....Big Ben pops up on TV and everyone yells We've been there!! I think it fuels travel possibilities.

-I've never quite understood the suggestion of Bath to get over jet lag. Your flight times from NC won't be as bad as mine from N. Idaho but after an international flight there is nothing I want to do less than get back on some kind of public transport for a couple of hours ride to my destination. I can manage an hour in to London on the tube but that's about it. (Don't get me wrong...I LOVE Bath! Just don't want to go there right after an international flight.)

-Last year I landed in London on a Sunday and after dropping my bags headed out to find the RAF Bomber Command Memorial in Green Park. I had a great walk thru the park with everyone else who was out for some air, wound my way thru to Buckingham Palace and then St James' Park. Then, as Rebecca indicates, had an early meal and early bed. It worked perfectly for me and I particularly like walking thru green spaces when I am needing to revive!

-In August I would get a hotel with AC. I've been there a couple of times in early Sept where it was pretty hot and needed AC to help with sleep so I would definitely want to hedge my bets against heat with AC in August.

This is going to be a wonderful time!

Neither supporting nor not supporting the Gatwick idea, but I thought only Norwegian, WOW, and Icelandair flew there conveniently from USA (except flights from Orlando FL)? Maybe I'm wrong about that.