Just a few comments on your proposed itinerary.

You are unlikely to want to visit either Manchester or Glasgow unless you have friends there or a specific reason. It's like going on vacation to Detroit (sorry Detroit!).

If you stop at York, don't just overnight there or you won't see anything. Allow a good day to see the old town, the Roman walls, the Minster (Cathedral), the museum, etc.

In Scotland instead of 2 days Inverness, 2 days Glasgow you might want to drift around eg 1 day Braemar, 1 day Inverness, 1 day Fort William, etc, all easy stages of a couple of hours each.

On the way back from Scotland you might want to break halfway in the Lake District.

Honestly, there are such a wide range of options, but these are some of the "standard" ones.