OTL, when the Maid of Norway succeeded Ned Longshanks was busy campaigning in Gascony as well as dreaming of a new crusade. Then she died, and Longshanks was asked to mediate between the rival factions. The English got mired up to the rims in Scots' affairs and Ned had to sign a treaty with the king of France and move his crusade idea to the backburner.
Now, for arguments' sake, let's suppose that the Maid of Norway doesn't die, and the English don't have to divert attention away from Gascony (or the crusade-idea). What happens next? Edward I most likely still remarries, although he originally wanted to wed the Scots' dowager, Yolande of Dreux, IIRC.