Get someone else to do most of the driving if you can. When I was in Scotland I went to see my cousin who now lives there. He was in 20s when he went to live there; he was driving here since he was 17 but took driving lessons over there before he got on the road. I got freaked out a few times at first sitting in the left seat thinking he was going the wrong way until I got use to it. The roads are a lot smaller there and the road sings are different, from what I remember they don’t have compass directions on their roads like east, south etc., but the name of a major town in the direction you can go.
Since I only sat in the passenger side I can't give any real advice. From what I had heard others say you can acclimate in a day or two of driving, you just have to stay real focused at first.
You can take trains to the cities and use taxis if you want as well so you can just stay parked some place.
Good luck in understanding a lot of the common people on the street there, especially where I stayed in Glasgow. They are real warm towards Americans.
Edinburgh is a very nice city, as is rural Scotland, enjoy your time there. I did not get over to Ireland.