Rethinking - if I drove in 4 lanes of traffic in rush hour Phoenix Arizona - comparison??
It's really incomparable tbh, virtually the total opposite! I think the only place in Scotland where there is 4 lanes of traffic each way is the M8 freeway through Glasgow.
Even the nearest freeway type dual carrigeway to Skye must be 100 miles away!
As Nigel says, if you're not generally comfortable driving in Scotland then I'd maybe consider whether you want to drive on Skye, as the roads there are arguably not that great and very twisty and narrow with single track and passing places in parts. Add to that the fact that they can have sheep wandering around on them and many of the other drivers are tourists who aren't used to driving on the LHS.
The flip side of this is that Skye is a fairly large island and public transport is very limited, so to get anything like the best out of your visit you need a car.
Overall, if you're not comfortable driving here then I'd reconsider driving on Skye - and if you are going to drive there then tbh you might was well have a car through most of your trip, because the other driving elsewhere will probably be easier than Skye, or at least not any worse!
For the rest of your itinerary I definitely agree about Inverness - Inverness is nice enough but you need to be bear in mind it's about a tenth of the size of Edinburgh and about a 20th the size of Glasgow and there's proportionally that much less to see. Most people would probably find 1 day - and in many cases half a day - is enough to see Inverness.
Wrt Pitlochry, it's a fairly long way from Inverness and it's probably just as easy to visit there by train from Glasgow to Edinburgh, as the journey time is virtually the same. Also, if you're taking the train from Inverness to Edinburgh this train passes through and stops in Pitlochry anyway. However the problem with trying to see it en-route is the fact you'll presumably have your luggage with you and I doubt there's any left luggage facility at Pitlochry station.
Either way, Pitlochry is a small town which you can see pretty quickly and most of attractions are outside Pitlochry in the countryside i.e. Blair Atholl Castle, distilleries, Dunkeld etc, so you've got to factor in how you'll travel between them without a car.
This is why tours with companies like rabbies may still be a good idea. I realise they don't fit the Skye portion of your trip, but they might fit for other visits in other parts of the country, because they will take you direct to the places and attractions you want to see - and transfer you between them - without you having to rely on infrequent or even non-existent public transport.
In the above case I'm sure Rabbies or other companies do tours going to Pitlochry and surrounding attractions from Edinburgh and Glasgow and this may well be a better option than going by train.
There is plenty to see in both Glasgow and Edinburgh and with a long trip I think you've got plenty time to visit both, so you don't need to pick between them.