While not "Battles" per se, the "15" and the "45" were historical conflicts that greatly altered the history of Scotland. The "15" is also know as the First Jacobite Rebellion and the "45" is also known as the Second Jacobite Rebellion. They occurred in 1715 and 1745, respectively. These conflicts take their name from "Jacobus", the Latin form for James.
The conflicts would have restored the Stuart kings to the thrones of Scotland and England, instead of the House of Hanover. They also would have had an impact on the religions of the two countries, since the Stuarts were Catholic, while the reigns of William and Mary and the Hanover Georges pushed Protestantism.
The Carruthers family lost the Rammerscales estate in 1745 due to fines imposed when Robert Carruthers, 4th Laird of Rammerscales, supported the Jacobite cause.
For details on the political and religious issues, see the Jacobite Risings section on Wikipedia.