Reasonable First time 2 wk itinerary?

Where are you coming from? Is this a trans Atlantic flight? If your flight arrives at 4.30 you will need to allow at least 1-2 hours to clear immigration, collect bags and make your way the tube or bus station to get to either Reading or Paddington station in London to get the train. Check out the National Express bus service, it’s just over two hours from LHR to Bath. I always used the bus to get from LHR to the West Country north of Bath where my Mum lived. Found I usually slept for most of the journey and it was a lot less tiring than coping with buses, tube and trains when jet-lagged.

You are trying to squeeze too much in in too short a time. The Cotswolds are a large area with a lot to see, how are you planning on seeing it and Stonehenge in one day? A local tour company, or renting a car? And then a train journey into London on the same day?

Have you considered flying out of Edinburgh (assuming you are headed to ) the States. This would give you more time in Edinburgh. Or alternatively, drop Edinburgh and stick to England.

I have been to London for a week with a day trip to Stonehenge, but think your questions are valid. The 6 days in London make sense to see sights and even do a day trip.

Why not start the trip in London for the 6 days rather than being jet lagged and going to Bath immediately? Or have the last week in London?
We enjoyed the day trip to Stonehenge on the train and caught a bus in town to go out to Stonehenge. It was fun and relaxing to take our time rather than be on a tour bus.

Can you fly home from Edinburgh rather than go back to Heathrow?
Looking at the map you are heading west, then east, north then south.

The day stop in York hardly seems worth it.

If you do the York stop and go to Edinburgh, you have one full day in Edinburgh, then catching a train to London.
If it were me for 12 days, I would do London and 2 of the 3 other places that are favorites.

I'm not sure where you are flying in from, but I would stay in London the first 6-7 days (including your Windsor day trip). By the time you get through immigration and then try to catch a train to Bath, it sounds like too much. Instead take the train into London and have a lovely dinner and stroll in London.
I'd find a Cotswolds/Stonehenge tour out of Bath, while you are staying in Bath. (Not sure, but maybe this is your plan?) Then you could catch a train from Bath to Edinburgh (via stop in London) remaining in your Bath accommodations and avoiding the one night London stay. Can't really speak for the York stop, and probably if you departed out of Bath there wouldn't be time to visit York and get to Edinburgh all in the same day. Seems like trying to cover too much with the York stop.
Lastly, I would have booked a multi-city flight, arriving in London (day 1) and departing out of Edinburgh (day 13), allowing a full day 12 in Edinburgh. (If there's a change fee or you just simply don't want to change your flights this trip, it's a good hint for future travel.) You will have a wonderful trip, however you arrange/organize it! (I'm curious what others will suggest too!)

We did a similar itinerary in 2015, but had 14 nights. Bath => Oxford => Edinburgh => York =>London.

We arrived a bit earlier at LHR than your scheduled time, but were still able to take Heathrow Express to Paddington, train to Bath, cab to B&B, and then walk into town for a late dinner. The coach may be more practical for you. Don't let those deter you who say it's too much to get to Bath on arrival day.

Your daytrip from Bath seems unrealistic - I think either Stonehenge or Cotswolds, not both, unless you're adding a night in Bath.

Then I'd suggest Oxford after Bath - it's two short commuter train rides. We left Bath at reasonable hour, and still arrived at Oxford lodging before official check-in time - 2 nights. Then Edinburgh from Oxford.

You are giving Edinburgh short shrift - it's a great city, and deserves at least three nights. I may be in a minority, but I still don't understand all the fuss over York [other than the railway museum]. There are plenty of large churches in London. So I'd skip York. BTW, Oxford and Edinburgh were the two favorite cities on our trip.

That should give you adequate time in London, with many options available. Also your plan wastes your last day back from Edinburgh, by going straight to the airport. If you leave Edinburgh in the morning, you can be in London mid-afternoon to start your time there. On our last day in London, we had time to walk to Victoria & Albert for a continental breakfast and a quick walk-through before retrieving our bags from our South Kensington hotel and getting on the Piccadilly line to LHR for an afternoon flight.

As for multi-city flights, no use crying over spilt milk.

Day 3 you plan a tour of the Cotswolds that includes Stonehenge? You are doing this from Bath, which means a lot of driving. We spent two days exploring the Cotswolds, not sure what you will see on your tour, but you will miss a lot.
Day 10, train to York, explore York for the day, what is left of it, then do the evening train to Edinburgh. This is the worst part of your planning. There is so much to see of York, we spend over three hours at the Minster (Cathedral) that included a wonderful tour. The National Railway Museum (at the train station is great and takes at least 2 hours to see). There are great museums that you will miss.
Walking the ancient walls will take a good bit of time. You need at least another full day in York (we did three nights there).
Days 11, 12, not enough time for Edinburgh.

I suggest cutting something in your schedule, perhaps you should just do England on this trip and spend the time you allowed in Edinburgh for York and perhaps Durham.

Going to Bath there is another way by train than going into Paddington and back out, or 2 trains to Reading, change for bath.
Most people have not recommended the Rail Air coach to Reading due to its cost and need for separate tickets.
However it has come to light this week that there are through tickets to all GWR and SWT destinations which are much less than the sum of the parts, so that becomes a very good and easy route.

We did a very similar itinerary 5 years ago, with the exception of less time in London and 2 nights in Oxford. It was not overly ambitious. Also, we never have difficulties getting through customs and then going on to the next place. I think landing at Heathrow and continuing on to Bath sounds just fine, although you will certainly arrive tired LOL
You might consider cutting your London stay short by one day and actually staying overnight in York. It's a delightful city!

Thank you all for the advice. I'm getting the sense I need to cut at least one thing. To answer a couple of the questions people have had:
1) we are arriving and departing from LHR on a transatlantic flight. tickets are already booked so multicity is out at this point
2) for the Cotswolds/stonehenge bit, this would be a pre-arranged tour of some sort. I dont plan to rent a car or try to do all that myself.
3) overall I'm trying to limit the number of hotel changes we make. My wife has patiently put up with my on-the-go "live out of a backpack" overseas vacationing. We're trying to be a little more stable this time. Looking for no more than 3 different accomodations basically.

I'm gathering from feedback that what I probably need to do here is probably drop Edinburgh.

Dropping Edinburgh makes sense as you aren't really allowing yourself much time there anyway.

Use the time to add to York - not only is there so much to see and do in the city it is also a good base for seeing more of the area. Have a look at either BOBH Tours or Glenn Coaches both offer a good selection of day trips allowing you to see some of the amazing Yorkshire scenery too - either a day trip to the Yorkshire dales or the Moors and coast at Whitby... It will be very diffgerent to what you have seen earlier in the South. Durham with its castle and cathedral is only a short trip on the train too. It is a small compact city and easily walkable. (There is a shuttle bus from the staion to the castle and cathedral.)

Or you could reverse the itinerary and put in a giant short cut.

After your Cotswolds etc day fly from Bristol to Edinburgh, there is a late evening flight on Easyjet most days at around 9pm, which is often as low as £25 before baggage fees etc.

Then divvy up the other 9 days between Edinburgh, York and London in that order.

A far more sequential progress.

The last direct coach from Heathrow to Bath is at 1825. But the last Rail Air to Reading/train connection is as late as 2224- 1/2 hourly before then.
The overall journey time is just under 2 hours.

The through fare (Coach and Rail) on a Super Off Peak Single is £52.90 on any train. On trains after 1929 from Heathrow there are advance fares of £36.60- on a specific train.

But the £52.90 is valid on any train, a walk up and go fare.

And this is the Bath to Bristol Airport bus, taking 75 minutes (or under the hour off peak)- hourly from 3am to midnight- https://www.airdecker.com/wp-content/uploads/2022/04/Timetable-2022.pdf

So you could equally overnight in Bath, then take the first flight at around 7am next morning to Edinburgh and still have a full day there.

Just a few thoughts: Although you'll be tired, I'd suggest using that foggy-eyed first afternoon to travel by train to Bath. Spend 3-4 nights there so you can really explore the town and overcome jetlag in a setting where you can reach everything by foot. MadMax Tours are small group van trips that are an easy way to see the outlier sites such as Stonehenge.

I love the city of York and have visited there multiple times. BUT, it's a long train trip from Bath or London. If you have your heart set on visiting York, stay for 2-3 days so you have time to enjoy the sites.

End the trip in London. You really need to be in the city of departure the night before your flights to ensure you can make that trans-Atlantic flight home, so save the London (and London daytrips) sight-seeing for the end of the trip.

A suggested alternative itinerary: Arrive at Heathrow and travel to Oxford. There is an Oxford bus that leaves from Heathrow and goes directly to Oxford. Keep in mind that "bus" in this case is really a more comfortable "coach" type travel. Stay in Oxford for 2-3 nights. Then travel by train to Bath and end in London.