WI Alexander III had a posthumus son in 1286?

In OTL King Alexander III of Scotland married his second wife Yolande de Dreux in 1285... By that time he had no male heirs... His firstborn son Alexander had died aged 20 in 1283 while his second son David died aged 9 in 1281... Both sons were from his first marriage with Margaret of England daughter of King Henry III...
In 19 March 1286 the King died while riding to visite his queen... Yolande was 2 months pregnant at the time...
In November her pregnancy ended in a stillborn child... causing an interregnum while the Guardians of Scotland governed the country...
WI Yolande had given birth to a posthumus son (lets call him Alexander IV)
How is that altering History? Could Edward I of England controlled Scotland as he did in OTL with the Guardians of Scotland? Who would be the infant King's Regent? Any thoughts?
 
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