My daughter has never been to Scotland and is interested in a 2017 trip. I, however, just spent 10 days there in May. It's been a couple of years since I've been to Edinburgh so I'm thinking a happy compromise would be to fly into Edinburgh, stay there 4-5 nights (show her Edinburgh & maybe a day trip or two) and then travel to another country for the last 4-5 days. I would think Amsterdam fits the bill but I know there are other possibilities. We've already traveled England together so I'd rather not do that. I love the wisdom of the RS boards because invariably options emerge that I would never have thought of... thanks in advance!
You can pretty much pick any place in Europe and be there in a few hours with a flight from Edinburgh. What are you most interested in seeing? Quaint towns? Museums? Nature? I loved Amsterdam and think you can't go wrong there. Totally different than Edinburgh, plus you can take a side trip to some smaller towns. A few places on my bucket list are Prague, Budapest and Dubrovnik.
If you fly Aer Lingus, the easiest additional country is Ireland. You can connect through Dublin or Shannon.
Scotland has historical connections to France (Mary Queen of Scots, for instance) so there's always Paris. Or you could pursue a Viking theme and go to Scandinavia.
I've comboed a trip to Scotland with the Netherlands so I know it works. But, I have to do a pitch for Scotland. If you didn't get to Orkney on your visit, you might think about a visit to the Orkney or Shetland as part of your trip. They are quite different from the rest of Scotland and so would give you variety, but would still have a bit more of Scotland for your daughter.
Pam
Prague, takes 2 hours to fly from Edinburgh
Piggybacking on Pamela's suggestion to see more of Scotland, if you want an urban destination, you can't beat Glasgow. It's got lots of energy, lots to see and do, and is VERY different from Edinburgh (as different as New York City and Washington DC). If you want some ideas, here's my report of my recent trip: https://community.ricksteves.com/travel-forum/trip-reports/uk-trip-report-glasgow-manchester-liverpool-in-september-2016