OTL, Longshanks was possibly the greatest King of England (despite what a certain Yank born Aussie w.ould have you believe). Subjugated Wales, almost did the same to Scotland. What can eliminate the "almost" from the previous statement.
Lets give him a few more years of health, in 1307 he defeats Robert the Bruce (OTL he was going on a campaign against him when he died) and English control over Scotland is strenghtene. Its idiot-proof, when Ed II takes over the rebellions do not end English authority and the matter is settled forever when Edward III shows up. Scotland is incorporated into the Kingdom of England, like Wales was.
How dose this change history. Bright side; no Braveheart!