scotland, ireland, wales

Right off the bat I'd say 15 days is too short a time for all 3.

All 3 countries are a bit harder to do with public transport if you want to see some of the sights in the countryside. Do you have sights in mind in each country that you want to see?

Have you considered a tour? I've done Rick Steves tours of Ireland (14 days) and Scotland (11 days) plus a Road Scholar tour of Wales (12 days). The RS Best of England tour also stays 2 nights in Wales so you can see a couple of things.

Agree, 15 days is not enough even for a blitzkrieg, whirlwind, drive-by. Not a great choice IMHO. And if you're not going to drive, and want to go entirely via public transport, that's going to slow you down substantially, too, and makes "15 days" even more untenable (all of these areas are arguably best done by car). And not to beat a completely dead horse, but you say "Plan to be gone 15 days." That means you actually have just 12 or 13 days of usable time once you get there. With that short a trip, many wise travelers would suggest you should pick just one of these, not even two of them. Sorry, I know that's not what you want to hear (but is does simplify your question about which order to do them in....if you only pick one). If it were me, I'd pick Ireland.

I haven't been to Ireland. With the amount of time you have, you'll have to make painful decisions in Scotland even if you limit your trip to that single country. I say that as someone who spent 26 nights there this year, partly accompanied by someone who had only 19 nights, so I've had the experience of trying to see a good variety of Scottish destinations in a short time. While I wouldn't say no one should go to Scotland if they have only 12 or 13 nights, it will be a challenge in that amount of time. And it is definitely true that not driving complicates matters, especially when you travel west or north of Inverness.

I've only seen northern Wales and Cardiff, and I didn't travel through the middle of the country to link the two. My impression is that public transportation will be somewhat limiting there but not as challenging as in Scotland.

I think you need to separate the countries into three trips if you are limited to 15 days door-to-door. Note that these are not contiguous countries. Getting to Ireland will require a ferry or a flight, not a quick, simple train ride. Personally, I hate having to get on a plane in the middle of a trip because of the time required to get to the airport early to allow for security procedures, etc.

There's a great saying: "In America, 100 years is a long time. In Europe, 100 miles is a long distance." I first heard that from one of Rick's Irish tour guides, interviewed on Rick's radio show. Everyone who has been to Ireland really emphasizes just how much longer it takes travel in Ireland than a comparable distance would take in the US - and that's with a car.

If you really want to see as much as possible in the short time you have, look into an escorted tour. Because someone who knows the way is taking you from place to place, you can see more in less time than you can doing it on your own.

If you want to do on your own, you have to cut WAY back on what you plan to see. Remember that two nights in a place only gives you one full day, and that it takes a half day or more, end to end, when you change from base to another. Furthermore, without a car you'll be tied to bus and train schedules, and the more rural the area, the less frequent these will be, meaning you will inevitably have to spend more time in a place than you intended, just waiting for the next bus.

Do look into flying into and out of different airports. On a short trip, this saves a lot of time backtracking.

We did S. Wales and England and it took 4 weeks and we didn't go to London or SE England.

Eliminate one country.
Don't miss Tenby in South Wales. Also, go to St. David.