I've not done the tour, but I've visited Scotland quite a bit and there is usually a fair bit of walking. Edinburgh itself is quite hilly, but you may want to look into ways to make sure the walking is for the actually touring rather than transportation from place to place. For example, they start day 2 with a "hike" through history in the National Museum. I suspect that they call it a hike as you start on the ground floor with pre-history and the 21st century is on the top floor and so you are climbing through time as it were. The next stop is the castle. I bet that they walk it. You might want to do a taxi so that your mother can save her legs for the Castle itself. There is climbing in the castle so you might want to check this out. I don't know where he's taking you in the Cairngorms, but there are a lot of lovely walks that go around the lochs and not up the braes. :) You really have control of the walking at Culloden. Cawdor Castle is not a huge place and the gardens are beautiful, but not huge either. Urquhart Castle is a ruin, and so , once again you can control how much up and down and clambering around you do. There is a nice visitor center with a film on the story of the castle. When you go to Iona, you do have to walk to the Abbey from the ferry, but it looks like you can pre-book a taxi. And lastly, you may want to check into this for Stirling Castle.
It's a beautiful, friendly place and I hope you both have a wonderful trip.