Traveling with 2 children to Great Britain

Just curious. For the longer stays, are you getting rental flats?
In London there are many amazing parks and neighborhood parks. You and your children could enjoy exploring these as part of your days.

Do the Himalayas putting green at St Andrews.

We're staying at friends' homes in London and Blenheim but they won't be there when we're there.

We're in Durham at the moment visiting our son who's at university here, and went to Beamish today. Your kids will absolutely love it. This was our second trip (we were there in January) and it's probably the best attraction of its type that I've ever seen, anywhere.
We love Durham. Yesterday we went to Bishop Auckland and saw Auckland Castle, residence of the prince bishops of Durham. That, together with Beamish, Durham Castle itself (when open for tours) and Durham Cathedral, will keep you very busy.
You might want to consider return your rental car in Durham and taking the train straight to York.

The scenery in the Highlands is different to the Lake District, but it may not appeal to your children after 2 similar consecutive stops.

I am not a fan of one night stops and you have quite a few of them, so I would be tempted to head straight to Edinburgh and claw back 2 nights. You have 5 nights set aside for Edinburgh, which is only 4 days, which is to include 2 day trips, so you won’t get to see everything in Edinburgh. Add a night would be my suggestion.

I wouldn’t bother with St Andrews unless you are golf fans - it’s a pain to get to by public transport - a train then a bus from Edinburgh (2 hours each way door to door - not ideal with children). Instead, take the 30 minute train ride to North Berwick on the coast - a pretty, upmarket seaside town - your children may like the closeups of mammals and birds at the Scottish Seabird Centre, take a walk on the beach, scale The Law (hill with wild ponies) and enjoy the many cafes and restaurants for lunch.

Again, you only have 2 nights (1 day) for Durham. Beamish is a full day trip. Add a night here.

York - the National Railway Museum is worth a visit.

You may struggle to find accommodation in some of the more touristy areas if you are travelling July or August. August in Edinburgh means the Fringe Festival and some places are booked a year in advance.

Driving to Oban and then on to Inverness seems like a very long drive in two days, fabulous scenery but I would think you need to break it up a bit. Presume you will drive the motorway from Penrith to Glasgow, then the A82/85 through the Trossocks to Oban? I’d plan for an overnight in either Glasgow, and see whatever you want to see there and drop the day trip from Edinburgh, or at Balloch, Arden or Luss on Loch Lomand. Oban to Inverness will be a long drive but interesting - hunting for Nessie, Urquhart Castle etc. Or rather than stay in Oban you could continue on tha A82 through Glen Coe and spend the night at Ballaculish, much nearer Loch Ness. Glen Coe is beautiful and very atmospheric whatever the weather.

Stonehenge and Avebury are both large stone circles. I think the kids will enjoy Avebury more as you can walk within the circle, get up and personal with the stones: there always seems to be at least one person hugging a stone or communing with one! You also have the village within the circle, a Tudor manor house, and the great processual Kennet way marked by more standing stones. It’s also a lot less crowded and touristy than Stonehenge and you cannot get in among the stones.

You mention three major cathedral towns within what appears to be three days; all are old, all are beautiful, and all are full of history. Your plan of Bath to Wells, to Avebury to Blenheim might be a cathedral too far. Salisbury is the quintessential English cathedral, it has one of the four original copies of Magna Carta (dating to 1215), the tallest spire in England, is a stunningly beautiful building both in and out. Winchester is interesting, burial place of the Anglo-Saxon kings of England and Jane Austen. If I had to pick one it would be Salisbury.

Pick up a book like "Let's Take the Kids to London" (or search Amazon for "London Kids" for other similar books).
A few things I remember from taking my kids 20 years ago: eating at Yo! Sushi where food passes your table on a conveyer belt, seeing a real crown and real jewels at the Tower of London, seeing a Real palace (Buckingham), formal tea time with all the fancy foods, London street markets.

Are going to be in Edinburg for the Fringe Festival in August? It a fabulous event for all ages. Just making sure you know it's happening.
Safe travels!

We bought that childrens’ guide to London and it was wonderful to have and use with our grandkids.. When in Kensington Gardens look for the Peter Pan statue.