Of course the Roman advance stopped at the line across Britain where they constructed two walls, the most famous of which is Hadrian's.
Apparently, the goal of defeating the Scots and controlling all of the island wasn't worth the losses in men and treasure.
That left the Scots as one of the few European groups that were never subjugated by the Romans.
In the context that you use the word, "The Scots," you should not capitalize it.
Because, at that time, as I've tried to explain and explain, ad nauseum, is that "scot" was a Roman descriptive word for a behavior by some humans. Not a proper noun to identify a country, a nationality, a governmental type or even an organized military...
It was a word used by the Romans to describe a behavioral type of person who was not conquered by the Romans who lived in unconquered land in Britain. Since the Romans perceived "Rome" as the epitome of civilization, and "Rome" was to Romans a proper noun for a form of government (not a race, per se, other than to be a citizen of Rome or not posed great distinction to the Romans within a status ideology), then anyone who would "refuse" -- so to speak -- to acknowledge the (superior, to the Romans) government authority of Rome, then you'd be a cad, a stupid, a savage, a "scot."
While I don't know if the term, "scot" was synonymous with "stupid/savage," I do know that the term, "scot," was used by the Romans to describe those who were not conquerable -- given that Romans would not likely admit that they lacked power/authority to conquer, they laid fault on those who "failed to submit," and the like, placing a negative upon those not submitting to Roman authority...
Thus, all those not submitting in Britain, fierce, unconquered, were the darn "scots."
And, the word later became incorporated into the local language from a point of bravery and pride: "we're the scots, we're the people who would not submit to the Romans, and this is our land, this is scotland," later called, popularly and because of that officially later still, "Scotland (a noun)".