Bon jour encore, bucephale,
The kids would love the Museum of Childhood in Edinburgh. It's on the Royal Mile, and it's free. People's Palace in Glasgow would be of interest as well, if you get over that way. It's free as well. The Riverside Museum in Glasgow has a transport section that would be of interest to both kids and adults. The Elgin Museum has some really interesting displays, if you pass through there on the way to Inverness.
The Blair Drummond Safari Park, near Stirling, would be fun for the youngsters, as would the Highland Safari Park, near Kingussie. Both would be on your route from either Glasgow or Edinburgh to Inverness. And of course Nessie hunting on one of the Loch Ness cruises, although very "touristy," may hold their interest.
Unfortunately, many of the best beaches in Scotland are going to be out of your way. The east coast beaches, though not as stunning as their west coast counterparts, would be worth a visit if your itinerary changes. There are excellent beaches at St. Andrews, Lunan Bay, and Arbroath on the way north, and the beach at Aberdeen has one of the best amusement arcades/fun parks in Scotland, with roller coasters, a ferris wheel, and all sorts of rides. Unfortunately, the water is really cold at Aberdeen, so most people don't stay in the sea too long!
Just a bit north of Aberdeen is Balmedie Beach, which is unspoiled and normally very quiet. And just a bit farther up the coast is Newburgh, where there's not only a gorgeous beach, but hundreds of harbour and common seals. They are very curious animals, and will swim up quite close to you. If you get up to the Elgin area, Lossiemouth beach is spectacular as well.
Over on the west coast, the beaches on South Harris are absolutely stunning, especially Luskentyre and Scarista. They're the equivalent of any beach that you'd find on the list of the world's best beaches. They are completely unspoiled, and you could spend hours there, especially at Luskentyre, without encountering another person. But you'd need to get pails and spades for the youngsters, as there's not a whole lot to do there other than beachcombing.
Back on the mainland, Sandwood Bay has a two mile stretch of beach which ranks up there with the finest in Britain. There are also wonderful beaches near Durness and Golspie, and also at the western end of the Ardnamurchan Peninsula. Also, if you're taking the A830 from Fort William to Mallaig on your way to Skye, the beach at Camusdarrach, near Arisaig, is another one of Scotland's hidden treasures. Camusdarrach Beach doubled as Ben Knox's beach in the movie "Local Hero."
As Skyegirl has pointed out, you need to be aware of the protocol for the single track roads which you'll encounter in the Highlands and Islands. The main thing to remember is to be patient, keep to the left, even if the passing space is on your right, and allow yourself to be overtaken if someone is coming up behind you.
Okay, that covers beaches and some things for your children to do. I hope that gives you a start on your planning. Be sure to make your reservations early for Skye, and pretty much anywhere in the west.
p.s.: To answer your last question, yes, it's certainly possible to stay within a budget of around 200 pounds per day for the four of you. Obviously, your main expenses will be lodging and transportation. Expect to pay 80 to 100 pounds per day for lodging, which you can cut down by staying in chain hotels such as Premier Inn or Travelodge. Car hire would average around 30 pounds per day, plus petrol. Food would cost you as much or as little as you'd like to pay. Sometimes there's nothing better than eating a fish supper, while sitting on a pier watching the sunset