I love the Caledonia Sleeper! Which particular one though (Edinburgh/Glasgow/Inverness/Fort William are main options, IRC)?
There are two beds to each standard class compartment, so you'll need two compartments (one first class (single) and one standard class). It's a heck of a lot more expensive than a French sleeper or train couchette.
Man in Seat 61 is very useful for tips.
If you want to be able to hire a car then I'd suggest Edinburgh, Glasgow or Inverness. Fort William I'm not sure about for hiring, it'll definitely be limited. I've definitely taken the sleeper up multiple times but usually walked in or hitched lifts to mountains.
What time of year? In winter, unless you're winter mountaineering experience and equipped (ice axe and crampon use, white out navigation etc, and I would not take the 7 year old, keen 10 year old perhaps, and I'm pretty experienced) then Fort William and the Highlands wouldn't be much fun (or safe). Winter conditions are about October-April.
If they're Harry Potter fans you can go from Fort William to Mallaig, either on a normal Scotrail train or take a steam train - it goes over the Glenfinnan Viaduct (where the Dementors attack the train).
Actually the whole Sleeper leg from Glasgow to Fort William is stunning, (or misty, depending on the day). So set an alarm and wake early if taking this route.
Inverness isn't that exciting, especially if it's winter and you're not wanting close access to the mountains.
Edinburgh and Glasgow might be your best bet as there is plenty to do with children in both, within the city. You could then drive over to the other city, or driving 50 mins from Glasgow / 1h40 from Edinburgh would take you to the southern end of the Highlands, around Loch Lomond. A bit touristy, but stuff to do. You won't get much further north, Scottish Highland roads are long-winded (it takes 6 hours drive from Edinburgh to get to the northern Highlands!).
So... what time of year? which city?