Do you mean overnight or just a break from driving?
Reason i ask is that the road up is fairly straight forward and mostly motorway and would mean coming off the M74, in fact after you cross the border you are only about 90-100 mins away from glasgow.
Vote #3 for Moffat. Some decent hotels, nice B&Bs, good shops, and MOFFAT TOFFEE.
Ninabean, are you intending to come straight up the M74 or are you intending to cut through the Dumfriesshire hills and up through Ayrshire?
I ask because Wirral to Glasgow is about a 4 hour journey, half-way being near the border. When driving up from London I always made one of my rest stops either Tebay in the Lakes or Moffat. In your case Moffat would make a good rest stop and lunch venue.
Were you striking west through the hills, I'd think again. If you're making a full day of your journey there are lots more options.
From Edinburgh you can take the A701 - which joins the M74 - at Moffat :-)
It's about 1h30 south of Edinburgh which is no distance at all if you're thinking of an overnighter.
There are many ways of spending more time on the journey south. You could (for example) visit East Lothian - superb coast, lost of small towns Like Gullane, North Berwick, Dunbar, Eyemouth, Berwick. You can travel up the river Tweed through the Border towns - Kelso (Floors Castle), St Boswells, Newstead, Melrose, Galashiels, Innerleithen, Traquair, Peebles. i.e. The Border Abbeys and a shedload of stately homes in the area.
Depending on how much you intend to stop, you could stay in Peebles, or you could press on before stopping for the night.
From the Tweed, there are two ways of getting to Carlisle -
From Peebles, the A72 goes West. Cut onto the B712 and visit Dawyck gardens. This road joins the A701 eventually and you end up once again in Moffat.
Impossible to provide further advice until you pin down your desired options ...
Why do you want an overnight stop on the way home? The journey time is short - probably no more than 5 hours. Wouldn't you prefer an extra night in Edinburgh? Is there a specific reason why you want an overnight stop?
Okay, I think your questions has been answered re stop off point, is there anything you want to ask re your visit to Glasgow or Scotland.............to make your visit memorable