Eurostar from London to Amsterdam

I think you should do some research to see if the sights there appeal more than the sights in York. I've done the London to Amsterdam train and it's pretty easy but you are looking at a 4+ hour rail journey vs a less than 2 hour trip to York from London.

When I plan I look at 2 nights just equaling 1 full day. For Amsterdam I'd want at least 4 nights for 3 full days.

Given that you are going to North Wales an obvious other place to add would be Chester. If you're interested in cities as well then you could very easily add Liverpool and/or Manchester as well, then just take a fast train down to London.

Personally I would also drop the Cotswolds and replace with some time in South Wales and/or the border counties - like the Brecon Beacons, Herefordshire, Shropshire or Powys. Or frankly anywhere in or close to Wales. For me prettier than the Cotswolds and much quieter.

Absolutely go to Amsterdam. The Eurostar will be relaxing and you can get a good sense of Amsterdam in that amount of time, so you will know what you want to return to do if you want. It will be a nice difference to your UK travels. Our first trip to Amsterdam was for a biking trip and we found we got a nice introduction with our full day in the city before we began biking. We returned years later for a week long visit. Amsterdam is a wonderful city. Your visit would be a wonderful introduction. If you can do 3 nights, even better as then you have two full days.

Be aware that there’s a recommended check-in time of 90 minutes in London for Eurostar to add on to your 4-hour train journey.

Also tickets need to be bought well in advance as they increase in price.

What I’m really saying is that sadly it’s a bit more time-consuming and complicated than just jumping on a train. I did it and loved it - but I went for a whole week.

EDITED after re-reading your question.

+1 to Golden Girl

Amsterdam is a wonderful destination, but it is not next-door to London.

There are many vlogs on Youtube about Eurostar, watch a few (make sure they aren't too old). The current consensus seems to be that things have gotten crowded and unpleasant because of the need to deal with border formalities.

And as noted, the pricing is VERY dynamic and there are several classes to choose from so buyer beware.

I would go!
I took Eurostar London to Brussels and back in December for just two nights.
Check in is indeed 90 minutes before departure, but the staff have it down to a fine art.
A few trains are boarding and leaving all around the same times, and they wave you into the line for Border/passport control just before the 90 minute mark for your train.
I found it very organised.

In addition to the aesthetic considerations, your plane ticket out of the UK contains
a slew of departure taxes and fees that tickets from other gateway cities in Europe
don't have. You may find that the cost of your journey to Amsterdam is partially
offset by a savings in the airfare (this is especially true when booking tickets with
miles, perhaps less so with $ if you hit it right).

Currently direct Eurostar services to Amsterdam leave at 0616 (so at St Pancras soon after 0430) or 1103, arrive 1615 due to the time difference.
So unless you get up at stupid o'clock you lose all of Day 11 travelling.

If you want to see Amsterdam, then you should go. As others have pointed out, it will take some time to take the train but it's not insurmountable and it also is a unique experience. As Stuart pointed out, there is a direct train that goes into the main station in the city that leaves at 6:16 am and gets into Amsterdam at 11:15 am. If you don't want to get up that early, there are later trains. The next direct train after the 6:15 one leaves at 11:04 am and arrives at 4:15 pm, but if you don't mind a transfer, you could take the 7:04 am that gets in at 12:53 pm. That involves a transfer in Brussels. You can check it out here: https://www.eurostar.com/us-en (the prices quoted are in US dollars, fyi). If it were me, I'd go for the "stupid" o'clock train, as that would give you an extra half day.

The other advantage to doing this is that Schiphol airport is much easier to fly out of than London's airports (and also easier to get to from the city). I love Amsterdam and there is so much to see and do there, and it's a beautiful city. And I agree with what shoeflyer said. There is a special tax that you pay when you depart from a London airport, and you would avoid that (that's why for my next trip, I'm flying into London and out of Paris). :-) And as Wray mentioned, try to get 3 nights there if at all possible.

We did this in March of '24, and it was totally worth it, we chose the afternoon option from St. Pancras which includes a quick transfer in Brussels, on the same platform, there was no dashing around the station. But, the food, seats, and bathroom options are much better than air travel, and very relaxing. The security screening process is very easy and short. But, as other posters have mentioned, this does take longer than it seems like it might based on the actual distance between the two countries.

You will be taking in a lot of the UK, I might take one day away from that itinerary so that you can have 3 days in Amsterdam, because it's a completely different culture and you'll be within approx 30 minute train rides to other super interesting areas. (and you can easily walk to the train station from most areas in the historic center) we only used an Uber to get our luggage to and from the train station and we used the lockers there to store our things the last day so we could explore after we checked out of our Air B&B canalboat (highly recommend this option as well).

If you're into art, it's especially worth it, as you can get a semi-private tour of the Van Gogh museum in the morning, have lunch, and then hit the Rijksmuseum highlights in the same day--they, along with several other museums are all basically on the same square. Highly recommend the Rembranthuis musuem, and his favorite pub across the street. Also, there is the Van Loon Museum which is a restored Golden Age canal house, and then there is the Canal House Museum as well--which is in a canal house but is a multi-mediat museum that focuses more on the actual development of Amsterdam as a global power, etc.. Amsterdam is super-walkable and Ubering is very easy as well. You're a 30 minute train ride from The Hague if you want to see even more art--and can take a semi-private day tour to see wind mills and other iconic sights.