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I've been to Ireland and did a 3 day weekend stay in Edinburgh during a one-month stay in London.
We drove from Dublin to the west coast and then down, making a large loop back to Dublin. Dublin is fine and about 15 minutes outside of Dublin you get the postcard vistas in all directions. The people were very nice. We took off without making any reservations, finding B&B's in every place we stopped. We took a ferry to one of the Aran Isles where Gaelic is the main language. It was wonderful.
Edinburgh is a great city, but I'm wondering how comfortable you'll be if walking is a chore. There is a lot to do there, including the castle, which is a must see.
I've not been through the Scottish countryside much, but a guy who was in London with us took his family through it in a rental car. He'd also been to Ireland. He described the difference as Ireland having a lush, green, gentle landscape -- very beautiful -- while Scotland's is much more craggy and violent looking, but still very beautiful, just different. If it were me I would do either Scotland or Ireland. Since you're only planning Iceland for a week, and you'll be dealing with jet lag, you'd get more bang for you buck and a more immersive experience in either of those two places.