It's nice when someone like James knows forum members interests.
Haltwhistle could easily do you for 2 or 3 nights, then drive up the A68 to Edinburgh.
But if you want to combine that with a bit of the Lake District I would suggest Penrith, which is on the M6 north, and has a surprising number of quality family run guest houses. You are half an hour from the Lake District and under the hour from Haltwhistle and the best bits of the wall.
But the fact that you are going to Chichester suggests you are a bit deeper into the Romans.
So I would suggest 3 nights in Cockermouth- it's 30 to 45 minutes west off the M6, a market town just on the edge of the Lake District beyond Keswick. Cockermouth itself is more about the Wordsworths.
But of course the Roman fortifications came down the coast from the end of the wall at Bowness on Solway all the way to Ravenglass.
15 minutes drive from Cockermouth is the Roman museum at Maryport, a coastal town which was a major roman fort. That is well worth a visit as is the Aquarium on the harbour. There are bits and pieces, like the saltpans, if you drive up the coast to Allonby.
On another day you could go south to Ravenglass, about 45 minutes. There are Roman sites to see on the way down there (like at Moresby), but at Ravenglass there are the bath house ruins. They won't detain you that long but it's a nice drive down and certainly worth seeing the ruins. Then you can either drive up the Eskdale valley or, far more fun, take the narrow gauge steam train (the Ravenglass and Eskdale Railway- colloquially "Ratty").
Eskdale is one of the lesser known valleys, not being easily accessible from the Central lakes, but is still beautiful and has a lot of great walking of all grades. You can pick up guided walks books from the Ratty gift shop. So that's a day that combines the Lake District and the Romans, but is that little bit different from the tried and tested norm.
We also have two good museums in Whitehaven- the Beacon which tells the general history of West Cumbria, and the Rum Museum. That is a thoroughly well told and immersive experience relating the former trade into West Cumbria from the West Indies, of spices and rum and other good things.
Cockermouth is also a very easy drive from the Western lakes of Loweswater, Buttermere and Crummock Water- the less visited lakes in the full majesty of the High Fells.
There is the whisky and gin distillery at Bassenthwaite (and Llamas), afternoon teas at Bassenthwaite Lake station or the Armathwaite Hotel and Spa at the end of Bassenthwaite Lake (a splurge hotel if you wanted to stay there).
More than enough for a short stop over. I think there's a week there of ideas!!
Then resume your journey to Edinburgh with a 30 to 45 minute drive up the A595 to Carlisle for the A6/M74 into Scotland.
The first part of that drive as far as Wigton was actually a Roman road. There was a Roman fort at Cockermouth- Derventio- recent major flood events have uncovered previously unknown archaeology relating to that fort and town.