Make time for at least a few days in Edinburgh - it's fantastic, so much to do- and remember that during the fringe prices quadruple and get booked up way in advance.
I have friends in Bruntsfield who save up their annual leave and go on holiday for a month. The rent for that month pays their mortgage for the next 6 months.
Fife is worth visiting- the East Neuk is very pretty and St Andrews is nice for a day trip. V&A in Dundee should be open by then, and not far at all.Also good chances of dolphin spotting off the east neuk and boat trips for the same from Dundee. Heading west, Stirling is worth a day trip - perhaps fit in a day there en route West.
It would be hard to do mainland Scotland AND the islands properly in just a fortnight. Don't get me wrong, American tourists do do this, and there are companies that will do it for you but it's very tick-boxy take-a photo-move-on. You could look at Rabbie's tours to get an idea of itineraries then DIY one.
There are probably 2 options for week 2: head North-ish and visit Oban then ferry across to Mull, making sure you do day trip to Iona. Dolphins pretty common around Oban. Mull is beautiful and fantastic seafood.
Alternatively spend some time around Glasgow which has great shopping and culture. Dippy won't be at the Kelvingrove by then, but it's fab and worth a visit, and then head down to Arran. If you don't fancy driving down there you can get a combined ferry and train ticket; the train stops directly in the ferry port. Auchrannie spa hotel in Brodick (main town on Arran and where the ferry port is) is lovely and recently refurbished. The spa is good and it's also family and dog friendly. Lots of things to do on Arran including climbing goat fell (not quite a munro), brodick castle, lochranza distillery and the machrie moors standing stones- usually deserted, gorgeous at sunset/sunrise and like a non-touristy mini stonehenge. Plus all the usual "artisanal" shops in and around brodick.
If you wanted to devote most of your holiday to the islands you can get a hopscotch ticket for the ferries (see calmac website) and pick your itinerary. I've been to almost all the islands and Barra and Tiree are my faves of the smaller ones- if a bit desolate in winter! Great windsurfing off Tiree and again good chance of dolphins. Arran my favourite of them all though!
Disclaimer: I live in Glasgow, work in Edinburgh, am from Fife and studied in Dundee. Just need a secondment up to Aberdeen and I'll have most bases covered 