I've only ever flown to Askernish. If you're in Dornoch, I'd think the quickest way to get there would be to take the Inverness-Stornoway-Benbecula route that Loganair runs (sold under the Flybe banner - Loganair became a Flybe partner when BA pulled out of the Highlands a few years ago).
If you really want to drive, the best way would be to go to Uig on Skye via tha A890 and the Skye Bridge, and then take the Lochmaddy ferry (crossing time one and threequarter hours). Google maps reckons it's about 150 miles to Uig. It would be a beautiful drive, and in my opinion Skye is the nicest of all the Scottish islands. With your wife in tow, I'd look to spend a day or two on Skye (go to Elgol and take the Bella Jane boat trip across the bay to Loch Coruisk in the middle of the Cuillin, Scotland's greatest mountain range, visit Dunvegan Castle. Eat dinner at the famous Three Chimneys restaurant near Dunvegan, and stay in one of their rooms if possible.
Lochmaddy is on North Uist, so you'll then have a bit of a drive to Askernish. The Uists and Benbecula are joined by causeways. You'll see the religious divide of the Hebrides up close - North Uist is Presbyterian, of the rigorous Scottish variety, while South Uist is Catholic (and Benbecula is half and half).
You'd have to go back to Glasgow, but the most picturesque way to Askernish is the flight to Barra, then a short ferry ride across the sound. Barra is the only place in the world where scheduled flights land on a beach. I've never flown into it, but I really want to.