Question: Which rebellion did Sir John Wedderburn and Charles Edward Stuart fight for that ended with defeat at the Battle of Culloden?

Context:
Lost portrait of Charles Edward Stuart
The "lost portrait" of Charles Edward Stuart is a portrait, painted in late autumn 1745 by Scottish artist Allan Ramsay, of Charles Edward Stuart, also known as the Young Pretender or Bonnie Prince Charlie.
Charles Edward Stuart
Charles Edward Louis John Casimir Sylvester Severino Maria Stuart (31 December 1720 – 31 January 1788), commonly known in Britain during his lifetime as The Young Pretender and The Young Chevalier, and often known in retrospective accounts as Bonnie Prince Charlie, was the second Jacobite pretender to the thrones of England, Scotland, France and Ireland (as Charles III) from the death of his father in 1766.
 This claim was based on his status as the eldest son of James Francis Edward Stuart, himself the son of James VII and II.
 Charles is perhaps best known as the instigator of the unsuccessful Jacobite uprising of 1745, in which he led an insurrection to restore his family to the throne of Great Britain.
 The uprising ended in defeat at the Battle of Culloden, effectively terminating the Jacobite cause.
 Jacobites supported the Stuart claim because they hoped for religious toleration for Roman Catholics and because they believed in the divine right of kings.
 Charles's flight from Scotland after the uprising has rendered him a romantic figure of heroic failure in some later representations.
 In 1759 he was involved in a French plan to invade Britain, which was abandoned after British naval victories.
Sir John Wedderburn, 5th Baronet of Blackness
Sir John Wedderburn, 5th Baronet of Blackness was a Perthshire gentleman who joined the 1745 rebellion of Charles Edward Stuart and, captured at the Battle of Culloden, was afterwards convicted of treason.
 He was hanged, his estates were forfeit to the Crown, and his family was attainted.
John Wedderburn of Ballendean
Sir John Wedderburn of Ballindean, 6th Baronet of Blackness (1729–1803) was a Scottish landowner who made a fortune in the West Indian sugar trade.
 Born into a family of impoverished Perthshire gentry, his father was executed for treason following the Jacobite uprising of 1745, and the young Wedderburn was forced to flee to the West Indies, where he eventually became the largest landowner in Jamaica.
 In 1769 he returned to Scotland with a slave, one Joseph Knight, who, inspired by Somersett's Case in England, in which the English courts had held that slavery did not exist under English law, brought suit against Wedderburn for his freedom.
 Knight won his claim, establishing the principle that Scots law would not uphold the institution of slavery.
 Wedderburn ended his days as a wealthy country gentleman, having restored his family fortune and recovered the title Baronet of Blackness.
The Skye Boat Song
"The Skye Boat Song" is a Scottish folk song, which can be played as a waltz, recalling the escape of Prince Charles Edward Stuart (Bonnie Prince Charlie) from Uist to the Isle of Skye after his defeat at the Battle of Culloden in 1746.
Culloden Tower
Culloden Tower was built as a parkland ornament or folly in about 1746 on the estate of John Yorke MP, at Richmond, North Yorkshire.
 It is also known as The Cumberland Temple, in celebration of the victorious Duke of Cumberland's army over the forces of the pretender Prince Charles Edward Stuart at the battle of Culloden in 1746.
Jacobite rising of 1745
The Jacobite rising of 1745 (Scottish Gaelic: "Bliadhna Theàrlaich" ] , "The Year of Charles") was the attempt by Charles Edward Stuart to regain the British throne for the exiled House of Stuart.
 The rising occurred during the War of the Austrian Succession, when most of the British Army was on the European continent.
 Charles Edward Stuart, commonly known as "Bonnie Prince Charlie" or "the Young Pretender", sailed to Scotland and raised the Jacobite standard at Glenfinnan in the Scottish Highlands, where he was supported by a gathering of Highland clansmen.
 The march south began with an initial victory at Prestonpans near Edinburgh.
 The Jacobite army, now in bold spirits, marched onwards to Carlisle, over the border in England.
 When it reached Derby, some British divisions were recalled from the Continent and the Jacobite army retreated north to Inverness where the last battle on Scottish soil took place on a nearby moor at Culloden.
 The Battle of Culloden ended with the final defeat of the Jacobite cause.
 Charles Edward Stuart fled with a price on his head before finally sailing to France.
Battle of Prestonpans
The Battle of Prestonpans was the first significant conflict in the Jacobite Rising of 1745.
 The battle took place at 4 am on 21 September 1745.
 The Jacobite army loyal to James Francis Edward Stuart and led by his son Charles Edward Stuart defeated the government army loyal to the Hanoverian George II led by Sir John Cope.
 The inexperienced government troops were outflanked and broke in the face of a highland charge.
 The victory was a huge morale boost for the Jacobites, and a heavily mythologised version of the story entered art and legend.
Ogilvy-Wedderburn baronets
The Wedderburn, later Ogilvy-Wedderburn Baronetcy, of Balindean in the County of Perth, is a title in the Baronetage of the United Kingdom created in 1803.
 The baronetcy is a revival of an earlier title held by the family, which had been forfeited in 1746.
 John Wedderburn was an advocate and Clerk of Bills.
 On 9 August 1704 he was created a baronet, of Balindean in the County of Perth, in the Baronetage of Nova Scotia, with remainder to his heirs male whatsoever.
 On the death of the third Baronet in 1723 the title was inherited by Alexander Wedderburn, the fourth Baronet, who was the nephew of the first Baronet.
 The fifth Baronet was a Jacobite and fought at the Battle of Culloden in 1746, where he was taken prisoner.
 He was executed for treason in November of the same year, with his title and estates forfeited.
 However, his descendants continued to claim the title.
 On 18 August 1803 David Wedderburn, "7th Baronet of Balindean" (but for the attainder), was created a baronet, of Balindean in the County of Perth, in the Baronetage of the United Kingdom, with remainder, failing heirs male of his own, to the heirs male of the fourth Baronet of the 1704 creation.
 Wedderburn later represented Perth Burghs in the House of Commons and served as Postmaster-General for Scotland.
Prince Charlie's Cave
Prince Charlies Cave, is a cave where Charles Edward Stuart was said to have sheltered there for 5 days in 1746, when on the run from the Duke of Cumberland, after the defeat at the Battle of Culloden.

Answer: the unsuccessful Jacobite uprising of 1745