Is it wise to rent a home in one location in the high lands and then make day trips from there?

I would check the Scottish Heritage site to see which castles you might really want to see; and they do have a pass available. It may surprise you where most of the Castles are located. The West Highlands mountain and forest area is more natural and therefore has fewer castles, but is great for hikers, etc. Check the National Parks. A family with small children might enjoy an area with more activities available. Check other Skye postings and you will see that you may want to spend an overnight there.

The Scottish Highlands really don't lend themselves to a single location and then day-tripping, especially with small children. You might consider Broadford, which is convenient for Skye, Eileen Donan, Plockton, and as far as Glen Torridon. For the eastern end of the Great Glen, try to find something around Glenmorriston, which is convenient for Loch Ness, Culloden, and going into Inverness if you need shopping. For Glencoe, anywhere near Fort William is convenient. We have stayed in all of those locations on previous trips to the Highlands. Broadford and Fort William are both "market towns," and not especially photogenic, but the areas around them are quite scenic. The two towns offer restaurants, petrol stations, and supermarkets. There aren't many castles in the Highlands except for the fake Victorian types. The best area for Scottish Castles is east of the Cairngorms.

If castles are a principal interest, you might want to split your time between Scotland and the Yorkshire and Northumberland area of England, which overflows with historic castles. Buying an English Heritage family pass would probably save you quite a bit on admissions prices for castles.

Given your party size and age I would suggest a cottage or equivalent type of accomodation. However you will end up missing places. Highland Council covers an area similar to that of Belgium, and does not cover all the Highlands, these extend into Argyll and Bute, Perth and Kinross, Moray, they reach into Glasgow's suburbs.

If castles and the Highlands are important I would look at places in Argyll and Bute as well as Highland.

Your children are pretty young (I have grands that age) for more than just a couple of castles. On the west side of the great glen (Loch Ness) is Urquart Castle. It's all in ruins but well set up for clambering around. There's a good tourist shop, cafe, and good short video about the history. Later that same day, the kids might enjoy one of the Loch Ness monster museums. I can't comment on those as they weren't for us. A fun souvenir for the kids will be a stuffed "Nessie" and those are everywhere. We looped around the lake and stopped to see the locks in Fort Augustus. Kids would enjoy that. then we headed up the east side of the lake through quietly beautiful Scottish Highland country. Saw some Hairy Coos along the way (Highland Cows).
We happened to be staying for a week in a timeshare in Aviemore and were able to visit lots of whisky distilleries (our mission was different from yours). Aviemore is a small tourist town and well set up for it. Loch Ness is easily reached on a day trip. I would be tempted to based out of there if you're looking to spend a week somewhere. There are lots of nature parks and entertainment locations around Aviemore that the kiddos would enjoy. I would highly recommend taking them to see the Leault Working Sheep dogs - http://www.leaultworkingsheepdogs.co.uk/. The shepherd runs a show every day at 4 pm (except Saturday). The dogs are very friendly and the kids will have fun watching them herd the silly sheep. They could even help sheer a sheep!
You'll definitely want to spend a minimum of two nights on Skye if you decide to go. I'm not convinced that your little ones will get much out of it, though. It takes nearly four hours of driving from Aviemore to get to Portree. The natural sights are wonderful, but if it's bad weather or raining....a bummer - and the kids might not enjoy rambling around in a car. Just my opinion, of course.
We also spent a week in the Argyll/Bute area and I'm not so sure it's the best location for you. Castles and beauty - absolutely. But maybe not as good for little ones for an entire week. As two adults, we loved it.
You truly might want to consider spending a week in the York area. Alnwick castle is glorious for kids (and adults). Plus, they have the broomstick riding sessions (aka Harry Potter) that are as cute and fun as can be. Adults can participate. There's a large park/garden there (costs extra) and cafe. The town itself is pretty cute. Not too far away is another decent castle experience, but less so for kids, and a beautiful sandy beach. this is at Bamburgh (Bam burrow). Hadrian's Wall is also in that area and there's plenty of stops and museums in the area that the kids could enjoy. Lots of stones to run and climb on, as well as the history of the place. Hope this helps!

I suggest that you start by making a list of places that will appeal to your children and grandma. It may be that you need to divide your stay between two places--one up north and one further south. Or one in the East and one in the West.

Start by looking at this site from Travel with Kids. Mind you, I don't think that they are inclusive. For example, they miss out on Dynamic Earth. If you have any budding scientists or just love science museums, this one is great! I loved it and it was packed with lots of Scottish Children. I loved getting the Scottish perspective and there are tons of activities for kids. Second, they are missing out on some basics. What about the Zoo in Edinburgh? We don't have a panda here in NYC! They also don't always include outdoor activities. There are some great beaches for walking and wading and watching for dolphins close by Inverness and they seem to ignore them. (Culbin Sands and Chanonry Point. Here's a link to the Forestry Commission which has lots of outdoor activities to keep kids busy and happy. And they miss the Highland Folk Museum, which might be too old for your kids, that's your call! They also miss the Crannog Center near Aberfeldy. They had lots of children's activities when i visited. I am pretty sure school groups visit.

There are lots of resources for figuring out what castles you want to visit. VisitScotland has built out a "Castle Trail" which is primarily in Aberdeenshire. But there are castles elsewhere, although they tend to be in the central part of the country and on the coasts--think where were the battles fought? So, another place to explore this is Historic Scotland. Not all castles are listed, but a lot are--and the priories and abbeys as well. I love Stirling Castle. But there are many others that are fascinating. I have familial/ancestral interest in Dunrobin and love its gardens. Cawdor Castle has wonderful gardens as well. But Blair Castle has wonderful grounds and Glamis has great history and ghost stories.

Check out Undiscovered Scotland and look up the areas that you are considering and check out the towns. I've focused more centrally and east, but there are great places in the west as well. And I would do two nights on Skye.

Pam