If Edward did marry Margaret of Scotland, he might be able to bring Scotland into the Wars of the Roses on the Lancastrian side, or at the very least be given a few Scottish troops at a discount. Depending on how much he is given, it'd either increase the Lancastrian chances of a victory during the Readeption, or change absolutely nothing. There's also a chance that Edward and Margaret manage a child before the Readeption (in OTL Margaret of Anjou purportedly stopped Westminster from consummating his marriage to Anne Neville so that the marriage could be annulled later on), which means the Lancastrian cause could last longer than OTL. Though this does depend on whether their child is a girl or a boy. If it's a girl it is possible that the two Edwards come to an agreement to stop fighting by betrothing Edward of Westminster's daughter to a son of Edward IV, though I am not sure how likely that is, depends on Westminster's personality.
If Edward of Westminster does get the throne, then his reign could go in any direction. He could be like his paternal Grandfather and lead a series of successful military campaigns, making him one of England's most popular Kings. Or he could be like his maternal Grandfather's and try and fail to conquer/reconquer lands and territories. He could also be his Father's son and be an absolute waste for all.