WI: Dunkeld Dynasty Doesn't Lose Power In Scotland?

The death of Alexander, Prince of Scotland in 1284 led to the downfall of the Dunkeld dynasty ruling Scotland. His father, Alexader III, was unable to produce a new legitimate heir before being thrown from a horse and killed. The succession crisis changed the nation and eventually led to the Stuarts getting the throne down the line, with the last Stuart giving Scotland to England to form the United Kingdom.

But… What if something went differently? What if Prince Alexander lived long enough to at least have a son of his own? Or long enough to become King Alexander IV? If the Dunkelds remained in power, would the Act of Union even have happened? Would the Dunkelds become Protestant after the Reformation, and if the Act of Union never happened, would Scotland remain a rival to England? Would the Dunkelds try their hand at the Darien scheme? And possibly even succeed at becoming a colonial empire of their own?

I'd like to find out these and more, to see how much difference the deaths of a prince and a king really made.
 
I'd say that immediately, the war of independence is butterflied, the Comyns and Bruces might try something between themselves, but other than that I think a big change is no Auld Alliance.
 
Why wouldn't the Dunkelds ally with France? And even if the Comyns and Bruces tried something, would the Dunkelds still remain in power? I'm trying to see how long the Dunkelds would last if they didn't lose the throne with the death of Alexander III.
 
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