Although Scotland is a relatively small country it's not that small, it takes a long time to travel to places like Skye and Orkney, especially by public transport. The isolated and sparsely populated nature of these places means there is limited demand and the only flights are therefore on small (c.30 seat) aircraft at high prices.
With such limited time and budget I think Orkney probably just doesn't fit. I wouldn't personally do a day tour from Inverness, it must be hours of mostly sitting on a bus. A day trip to Skye is similarly long and I don't see how you can see much. Also, in both cases, but particularly Skye, if the weather is misty/overcast on the day you go (as is frequently the case) then you'll not see very much!
From Stirling to Skye is probably 7-9hours by public transport depending where you're going on Skye. You need to either go to Glasgow or Inverness then bus from there - Most public transport to the W and N Highlands goes from Glasgow and Inverness respectively, not Edinburgh. There is a direct bus to Skye from the forecourt of Glasgow airport at 1020 every day, so if you wanted to go straight to Skye on arrival that might fit well, although its a long bus journey after a flight like that. Lastly bear in mind that even once on Skye, public transport is limited so actually getting around to see some places could be quite a hassle.
I think in reality you definitely need to drop one of Orkney or Skye and I would maybe even drop both. I also wouldn't personally spend that long in Inverness itself - it's a nice enough place, but quite small and not all that much to see. There are plenty other scenic areas in Scotland that are easier to get to like Glencoe, Loch Lomond, Highland Perthshire (Pitlochry, Dunkeld, Aberfeldy etc), Aviemore etc. If you want to visit an island you could to to Oban and take trip to the likes of Mull or iona.
Long distance busses in Scotland are provided by Citylink, see www.citylink.co.uk for timetables/booking and www.scotrail.co.uk for trains. You might also want to look into the likes of Rabbies and Discover Scotland for tours.
Re GLA apt to Edinburgh, the advice given earlier for travel is unfortunately a little off target and overcomplicated. Take the 500 bus from apt to Queen St stn then get the train to Edinburgh - should take no more than 2hrs absolute max. You can also get off the 500 at Buchanan St bus stn and get the bus to Edinburgh, this takes longer but may be cheaper. Bear in mind there is a lot to see in Glasgow so it's worth spending some time there.