Perhaps the Jacobite Rebellion of 1715 succeeds. It only fails OTL due to the commander's incompetance. King James now acceeds to the Scottish throne and King George I of England makes peace with Scotland. James VIII pledges to give up all claim to the English throne, but his word is not taken at face value. England, in the middle of an anti Jacobite and Anti Scottish hysteria, starts to discriminate against expat Scots and suspected Jacobites and Catholics, who they fear is the enemy within. James in Scotland meanwhile declares limited freedom of worship. The Presbeteryian Church is recognised as the Established Church, but Catholics and Episcopalians are allowed to worship in their own way and are even allowed to build their own churches, although that is under strict regulation. Non-Christians obviously aren't allowed to worship. Many flee from England due to persecution.
France and Spain realise the value of a state on England's northern border, and court it with trade agreements, alliances, colonies etc. Scotland gets Darien, like they wanted, and advisors to train their army. Darien turns out to be a steady money maker, although many still die from Yellow Fever. Porters take goods across the Isthmus of Panama to load onto ships on the other side, and in time a canal is dug, with Dutch help. Other Scots trading colonies are set up on the African and Indian coasts, and in time they grow to be the start of quite a large empire (not as large as the British and French OTL, but a respectable size). There are more wars over the years with England, and Scotland manages to get Northern Ireland and the Isle of Man out of it (most of the population of Northern Ireland was Scots anyway). But England is often willing to pay such a price as it is involved with Continiental Wars. During the French Revolutionary and Napoleonic Wars, the Scots and English are both on the same side. Scots kings (who retain more power thna their English counterparts) are shocked at the Revolutionaries attempt to build a new European order. After that, despite some diplomatic tensions, relations between the states remain cordial. (WW1 and 2 may not happen here due to changing events, and this is only an outline. I've written enough).
So is this plausible?