A family history mentions that a set of my ancestors in New Brunswick, CANADA, spoke "braid Scotch", but I cannot figure out what that is. There are only a few mentions of the phrase online, but they provide no clear definition.
There is technically no such thing as the Scotch language, although that term was used historically. It is more commonly referred to as the Scots language.
Braid Scots (English broad Scots) is simply the vernacular (native dialect). This phrase alone does not localise the dialect within Scotland further.
What the author probably meant was: they could hardly understand a word of what they were saying when they spoke in "braid Scotch".