England, Scotland, and Ireland in 2 weeks.... Doable?

spreading yourselves too thin

If you really do want a taste of lands, peoples and cultures, just pick one country. Two weeks in a single country would not give you much of an in depth look. I have recently spent 4 weeks just in Scotland and didn't cover anywhere near half the country.

In 2 weeks you could manage the highlights of England, plus time in Edinburgh.
This, I think, is the best that you can hope for ...
London (4 nts)
Salisbury (1 nt) - pick up hire car
Bath (1 nt)
Cotswolds (1 nt)
Oxford (1 nt)
Stratford-on-Avon (1 nt)
Peak District (1 nt)
York (1 nt) - drop off hire car
Edinburgh (3 nts)

It is totally doable to have a "best of" tour in 2 weeks, but you will probably be focused more on city centres.

I would suggest starting in London with 4-5 nights, take the train up to Edinburgh for 3-4 nights, then take a cheap flight over to Dublin for the remainder.

Way too fast imho, spreading yourselves too thin. You'll "hit" your "obligatory sights" and "taste" your immediate surroundings, but you won't enjoy it as much or learn nearly as much as if you slow down and focus on a single country or region. I think two weeks would be a good adequate visit to Scotland or Ireland, and a good introduction to England or adequate visit to London. Not that you'd never want or need to return, but that you'd know enough to know whether and where to return, and have some great experiences and memories to show for your time.

Is there some reason you fear that this will be your only chance to visit these islands? If not, please consider making some choices and setting some priorities, and assume that you'll have other opportunities. I hope so anyway.

Remember the famous saying: "In America, 100 years is a long time. In Europe, 100 miles is a long distance."

England, Scotland, and Ireland may seem small by US standards, but it takes longer to get around them than getting around US places of comparable size. If you really try to see all three countries in 2 weeks, you will spend a lot of time in transit rather than in each place.

We did this last summer and it is spreading yourself thin, but we wanted to get a sense of the countries. We had done London before, so flew to Edinburgh, where we spent 3 nights. We then drove to Isle of Skye (beautiful but far) for a couple nights, then back to Edinburgh. Next we flew to Cork and drove to Kinsale for a couple nights then to Dingle where we went on the Sciuird Archeological Tour of Slea's Head. Kinsale and Dingle are super charming, great music, food etc. We skipped Ring of Kerry. Last we flew to Bristol and stayed in Bath where we stayed for 3 days. Went on the Mad Max tour of Stonehenge, Avebury & Cotswolds. Took the train back to London. Pat Connor, author of Ireland book, helped me plan it. Flying between those cites is easy and inexpensive. Check skyscanner for flights.

I'm in agreement with the previous poster that it's definitely doable, especially if you can stretch it to 15-16 days. It may be spreading yourself thin but for a taste of 3 countries that's fine. Just a suggested itinerary somewhat like the other poster's:

Fly into London - 4 nights with a day trip to somewhere outside the city, Bath or Windsor are good.
Train to York - 2 nights.
Train to Edinburgh - 3 or 4 nights with day trip outside the city.
Fly to Cork or Shannon and rent a car for 6 days, sightsee around western Ireland staying in Dingle, Kinsale, Killarney, Galway, etc.
Return car and fly home from Shannon. I would skip Dublin this time, it's nice but it's a big city not much different from London or Edinburgh and not a particularly good example of the differences between Ireland and the UK.

If you prefer to fly round-trip to London, you can drop car in Shannon or Cork or Galway and fly to London for last night before flying home.

You'll never be able to see everything you want in a 2 week trip anywhere but you can certainly hit the highlights.

I echo everyone else's comments and add this one:

I could keep myself occupied in London or Edinburgh for two weeks and STILL want to return for more.

We have spent up to month in England alone, and still haven't seen hardly anything. We can't wait to go back. We have been there five times for anywhere from a week to two weeks, each trip. We also did a two weeks TAUCK tour of Ireland. We are counting the days until we can plan another return to Ireland and England. My husband and I will never be tired of England or Ireland. I would find it to much of a tease to only have such a short time to see all those places.

For your first trip abroad I'd trim it to two countries as 14 days isn't really 14 days. Define in your mind what you TRULY want to see and do. Give yourself time to explore and ENJOY what you are seeing. Will you be driving or using public transport? Need to factor in drive times, flight times, train times or bus travel. Step back, calculate distances, define your itinerary then decide it you can see it ALL in 14 days.