Edinburgh was my favorite place to visit in almost all of western Europe, I would say you should definitely make it a part of your itinerary.
It is so cool to have the juxtaposition of the old parts of the city and the castle, right next to the modern parts of it. Scotland is simply beautiful in and of itself. The color of the rolling green hills simply does not exist anywhere I've seen in the States. Gorgeous!
I would recommend allotting at least one day of your trip to Edinburgh. Tour the Edinburgh castle, have a pint in a pub that is older than the United States, and DEFINITELY take one of the walking ghost tours. You get a great walking history of the darker side of Edinburgh and you get to visit some cool, creepy places. This was the one I've done several times and I just love: City of the Dead Tours - Edinburgh - Reviews of City of the Dead Tours - TripAdvisor
If you have a little more time to spend, a second day would be great to take a day trip out of Edinburgh. The trains will take you near anywhere in Scotland, and the train ride itself is extremely beautiful and is a to-do all by itself. I did this when I visited, took a train to Stirling and saw the William Wallace monument, did some shopping, ate some food, and hopped back on the train to Edinburgh before I took off again.
Not sure that you really need to drive anywhere. You should be able to trust the trains and buses and you'll have a much more enjoyable experience just sitting back and watching the landscapes as opposed to navigating the small roads and being stressed about driving on the left-hand side of the road. The train to/from Edinburgh/London is cheap, quick, and you definitely won't want a car while you're in London.
Definitely fit in Edinburgh and anywhere else in Scotland that you'd personally want to see. I don't think you need to commit a whole lot of time there, however, especially if you want to make it to London and Paris. All can be done satisfactorily in a day or two, but I personally wouldn't want to miss Edinburgh.