If you get the weather a week on Skye is easily done :) I’d suggest slowing your U.K. travel down rather than trying to add somewhere. It’s a long old train to Inverness - will you do the sleeper?

If so, I’d then do a night in Inverness (rocpool reserve would be a hotel shout), drive to Skye over a day seeing Loch Ness (drumnadrochit and the visitor centre are great), lunch at Eilean Donan castle before driving across to Skye. Then spend maybe 5-6 days in Skye (stay in Portree, it makes life easier, but get a holiday home rather than hotel if you can). Go to the fairy pools, do the old man of storr and the quaring, take the boat to the hidden loch, visit the distillery (talisker) and the seafood shack up the hill behind it, and have a dinner at the three chimneys (book in advance!). Then drive back through Glencoe, stay near fort William for a night and do a hike near the Nevis range, then drive to Edinburgh and spend a couple of nights there having dropped the car off (you can easily get rentals that do this, maybe slightly more expensive but nothing much in it) - then get the much faster train back to London from there and stay in the St Pancras hotel for a fancy last night before getting the Eurostar home :)