Thoughts on my itinerary?

I can understand if all the holiday you can spring is two weeks, but it is a bit rushed.

By the time you have been on the train from York for half a day there's won't be much time to see much of Oxford and that is a pity.

Two nights in the Cotswold area of Outstanding Natural Beauty and Site of Special Scientific Interest is only one full day for a fairly large area.

Is two days in London for your son enough for him to see what he wants to see, and giving a day to Windsor?

We have been to all the places that you plan to visit.
Generally, a good plan, but I have a few comments:

1) York is wonderful and we spend three nights there and had 2.5 days to tour. There is a lot to see. Our favorite places were the Minster (Cathedral) and the National Railway Museum. However, there are museums, walking the walls and taking in other things as well.
2) We spent a day in Oxford and enjoyed our free walking tour as well as walking around after. Still, Oxford can be done in one day.
3) We spent six nights in Chipping Campden that was probably one night more than we had to, but we were on a 28 day trip and needed to do laundry. We visited Oxford, Blenheim Palace, Stratford Upon Avon (this is a must see place) and the many towns and villages of the Cotswolds. You do need a rental car to see the Cotswolds. We stayed at the Volunteer Inn. You plan two nights, but are spending one in Oxford. I would plan on one day to Stratford Upon Avon and the other driving around all the towns of the Cotswolds. Rick Steves guide of Great Britain has a planned route.

4) Bath is great and we spent two nights there, but you can do Bath in one full day. We spent another day going to Glastonbury and Wells. While in Bath, don't miss a wonderful place for fish and chips. It is called the Scallop Shell.
https://www.tripadvisor.com/Restaurant_Review-g186370-d7375906-Reviews-The_Scallop_Shell-Bath_Somerset_England.html
Also, we stayed a the Brooks Guesthouse, a great B&B.

Your trip would be OK if the places that you want to see were close together, but you are going to lose so much time in transit, that it will severely impact on how much time you have seeing places, making your trip very rushed.

Personally, I would prefer to spend time in York than in the (overrated IMO) Cotswolds, but York is the the geographical outlier, so you may wish to consider dropping York. Oxford can be seen in one full day. The Cotswolds covers a large area and you have only allowed a day there (2 nights). It's personal taste, but I would also avoid the overly touristy Stratford upon Avon.

Dropping the car on arrival in Bath is very sensible.

Stratford Upon Avon is touristy, but if you love Shakespeare, you must go there.
You can visit the house where he was born as well as his tomb, his wife's home, mother's farm and the site of his house. Further, the city is loaded with historical buildings. We enjoyed it more than Oxford.

Is Windsor an absolute must? I’d consider dropping that to maximize London time and reduce some of the time you’ll be spending in transit. While this isn’t the most agressive itenerary, there’s a lot of time spent traveling. Otherwise, cut York since it’s the only sight up north.

Keep in mind that you’re going to be spending time checking in and out of hotels, gettting to and from train stations, and picking up and returing a car on top of parking and navigating.
There’s also the dead time when you can’t really do anything because you’re needing to be at a train station at a particular time.

I would argue that Oxford can be "done" in a day only if you have little or no interest in its two excellent (and very different) museums: the Ashmolean and the Pitt-Rivers. The town is relatively spread out, there are many colleges to visit but with different opening hours. There's a botanical garden worth seeing. The guided tour offered by the tourist office was good.

I have a different take on the Cotswolds, which I saw on a one-day van tour from Moreton-in-Marsh and really liked. If you don't have time (and cooperative weather) for some rural walking, I think a full day and perhaps a few extra hours with a car is fine. Coming in from Oxford and heading out to Bath--both quite near the Cotswolds--the OP could end up with some extra time in the area. The villages are mostly quite small. It doesn't take long to walk from one end to the other. You can see a lot of different places in a day, especially if you grab lunch on the go. After 4 or 6 or 8 little Cotswold villages, do you need to see more high streets on the same trip?

What would bother me about the itinerary would be the series of five 1- and 2-night stops. Plus I got bored with Bath's (repetitive) Georgian architecture after an hour; with two nights there I would have ended up regretting leaving York so quickly. But the OP has expressed an interest in history, so it may all work out.

Thanks to all who responded with some great advice! Looks like I was being a bit optimistic with my original itinerary, and based on the comments it appears I should eliminate York as one of the destinations and extend my stay in one or more of the other cities. Guess I'll just have to save York for the next trip!

One more question; with additional research it seems that it would be easier to return to Heathrow from Oxford than from Bath, so would reversing the order to London -> Bath -> Cotswolds -> Oxford be a better plan?

Parking in Oxford is very hard to find and expensive, so if you have a rental car to return at Heathrow, consider doing Oxford first. If you plan to return the car to Oxford, then going to Bath first would not be a bad idea.

If you rent the car at Oxford, then you might wish to return it at Oxford, unless you can get a rental without an extra drop charge.

Seems a shame to lose York, but I think your second plan, without it, will be a better overall trip because you won't be moving around as much.

I also think London-Bath-Cotswolds-Oxford makes more sense, get the car in Bath and return in Oxford. There's a direct bus from Oxford to Heathrow, The Airline.

If you want to see Windsor Castle, it would be more efficient to combine it with Heathrow, either after landing or before departing. A taxi from Heathrow to Windsor, or vice versa, isn't very expensive. There are also buses. You can leave your bags at the castle security checkpoint. You might spend your first night or your last night there, depending on your flight times. And there are good train connections to London or from Oxford (via Slough, rhymes with cow).