2 hours on Tuesday would mean staying down the Birmingham area. Or you could do tomorrow night in Liverpool, which is about 4 hours.
If you'd be up to doing 5 hours on Tuesday then I'd suggest going down the M6 to Penrith, then the A66 to Appleby for a stop, possibly. Appleby is about 45 minutes drive from Carlisle, then back on the A66 turning off at Brough onto the A685, calling in to Brough Castle (at Church Brough) 15 minutes away, where there is a very nice tearooms.
From there it is a very scenic 45 minute drive down to Sedbergh through Kirkby Stephen and Cautley (Cautley Spout- waterfall) should be in good flow after the recent rain.
Sedbergh is a picturesque small town, and a Book Town- lots of 2nd hand book shops.
There are a couple of hotels there- the Dalesman (a bit expensive) or the Black Bull.
Or you might like to push on another 45 minutes to the seaside village of Arnside- a nice place for your last night.
Or maybe down the old A6 through Milnthorpe and an overnight at Carnforth- several hotels in Carnforth. You could then have breakfast next day at the Brief Encounter tea room on Carnforth Station (Brief Encounter, as in the movie)- a nice place for your penultimate UK breakfast.
From Carnforth you're all but straight back on to the M6.
From either Arnside or Sedbergh it's about 5 hours down to Heathrow. From Carnforth about 4 1/2 hours.
Yes, I'm biased in trying to show you some of the less well known parts of Cumbria.
PS- I thought that if someone was staying in CD it rang a bell- you've been on your family history trail there. I presume you're doing stops in Dumfries, maybe Annan and maybe Gretna tomorrow. I've not heard of flooding at Whitesands but I imagine the river will be running high through the centre of Dumfries.
See if you've got time in Carlisle to visit Tullie House Museum and/or the Castle and the Cathedral if you have time.
I feel like I'm overfilling your day tomorrow!!