Regardless of how you get there and where England and Scotland go, it's going to be interesting times for the Anglo/Scottish Borderers. Given the history between the two countries, unless and until both Edinburgh and London decide to put some effort into law enforcement in the Borders, and manage to work out a mechanism by which miscreants can't escape justice by simply hopping across the border and daring officials to send heavily armed forces across the border in pursuit (and some Border raids in OTL could contain up to 3000 raiders, although most of the big raids were closer to the 300 mark), then you've got a lawless region separating the two countries.
Resolving this is going to be a problem; Scotland doesn't want to see big English forces massing on the border, and vice versa. But without big forces, the Borderers (who do not regard themselves as either Scottish or English and whose loyalty to either side lasts only as long as the pay holds out, or until they get a clear shot at the baggage train of either army) (1). Until Scotland and England build a degree of trust (2), the likely consequence is that both London and Scotland will see the borders as a sort of no-mans land between them. I'd call it a demilitarised zone, but given the nature of the locals, that doesn't seem entirely appropriate.
If Scotland is going on an Empire building spree, then it either has resolved the border issue (3), or it hasn't. If Scotland is going on an Empire-building spree, England is either going to follow suit, or is going to prepare to go after the Scottish heartlands. Or England and Scotland come to some sort of arrangement. (4).
It's a bit of a digression, but it seems to be an inevitable consequence of Scotland and England remaining separated.
1. Kudos to the Scottish Borderers at Flodden, who managed to win their bit of the battle, and then, when the Scottish King pleaded for their help against the English centre, decided it would be more productive to loot the baggage train of both armies before leaving the battlefield with the loot. Hume lost his head for that, but the rest of the Borderers made a tidy profit on the deal. The Scots lost the battle, but for the Borderers, that was an incidental matter.
2. Good luck with that.
3. Which might just involve letting the borders stew in their own juice and make sure trouble doesn't spill out, although this seems a risky option.
4. And obviously, no Scottish or English politician would ever go back on the arrangement.
