Succession in the British monarchy is, by law, determined through descent and gender, but also legitimacy and religion.

If Frederick had died without issue, that is, children, his title would have passed to the next son in the line, William, Duke of Cumberland. If William and Frederick had both predeceased George II without issue, only then would the daughters have been in the running. However, Frederick had a marriage to a Protestant, and therefore a legitimate son, George III, and several other children, so Frederick had continued the line, and his siblings had been effectively moved down in the line of succession. The same way Prince Harry today was no longer third in line after Prince William, his older brother and father's heir, had a child.

Through the laws of succession, Frederick's children were all ahead of their aunts and uncle in the line for the crown, because Frederick was the heir. George III was his oldest son, so George III was Frederick's heir. When Frederick died, George III inherited his father's titles. They were not redistributed amongst his aunts and uncle. This included the role of being heir. Now, again, if all of Frederick's children suddenly dropped dead after George III was crowned, with no issue amongst them, the crown would have gone back into Frederick's generation, specifically William, or, if William had died already, the eldest princess still living who was not married to a Catholic [marrying a Catholic removed you from the line of succession per the Act of Settlement ] since William had no legitimate children.

Another example of how gender influences who inherits would be Queen Elizabeth the first. While she was the second legitimate living child [hers and Mary's legitimacy was restored] she was the third to inherit. The youngest child was a boy, Edward VI, and he became king. [Why his named heir, Lady Jane Grey, was deposed in favor of Mary is a whole other thing]. Mary, the eldest girl, then became queen, and when she died without issue, Elizabeth I became queen.

So to summarize:

• Legitimacy [illegitimate children cannot inherit]

• Religion [Catholics cannot inherit]

• Gender [boys before girls]

• Order of birth [oldest to youngest]

Frederick was the legitimate, non-Catholic oldest son. He had a Protestant wife. So his titles passed to his legitimate oldest son upon his death, including the title of heir.

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There are a few reasons for this, but for this answer, I'll focus on one in particular: King George II not only became more favorable towards his grandson as heir after Frederick's death, but Prince William, Duke of Cumberland - Prince Frederick's younger brother - became more unpopular.

Or, in other words, often times, those heirs next in line to the throne having - or lacking - the royal assent, or approval, of the previous legitimate King or Queen would affect their own chances of becoming monarch. In the Tudor era, for example, King Henry VIII kept changing the royal succession to either exclude - or include - his three children, based on whom he favored most at the time.

Initially, King George II disliked his son - Frederick, Prince of Wales - and showed little to no interest in his grandchildren. However, in 1751, Frederick died unexpectedly at the age of 44; his eldest son, George, thus legally inherited his father's claim to the throne per the prior laws of succession, including both royal decrees and Acts of Parliament. Three weeks later, King George II reaffirmed his favor to Prince George by declaring him the new "Prince of Wales" by his own royal decree.

There are many reasons why King George II had disliked his eldest son, chief among them Frederick having developed a reputation for drinking, gambling and womanizing. Furthermore, once established in London as the Prince of Wales upon his father's own accession to the throne as King George II, Frederick sponsored a court of 'opposition' politicians, earning his parents' ire and dislike by playing "Devil's Advocate" during his father's rule.

Due to this, King George II originally favored Prince Frederick's younger brother - Prince William, Duke of Cumberland - and looked into ways where Frederick would succeed only in Britain, while Hanover would go to William. Frederick, too, was close friends with court gossip John Hervey, 2nd Lord of Hervey; however, after the two had a falling-out, Hervey called Frederick "false...never having the least hesitation in telling any lie that served his present purpose".

Frederick, too, earned the ire of King George II by repeatedly pursuing negotiations for his own marriage outside of the King's royal assent and authority. He did do firstly with Wilhelmine of Prussia, Margravine of Brandenburg-Bayreuth, his cousin, and the daughter of King Frederick William I of Prussia; and secondly, with Lady Diana Spencer, daughter of Charles Spencer, 3rd Earl of Sunderland and Lady Anne Churchill.

Both times, Prince Frederick publicly embarrassed his father, King George II, when he pursued marriages to both women on his own accord, without the knowledge, nor approval, of the Crown. In the case of Wilhelmine of Prussia, a marriage alliance between Great Britain and Prussia had been an ambition of King George II for many years; however, Frederick's flouting of his father's will may have contributed to the match eventually falling through.

Eventually, a 29-year-old Frederick married 16-year-old Augusta of Saxe-Gotha-Altenburg on 27 April 1736, upon Queen Caroline's insistence that Frederick find a wife, and try and mitigate his womanizing ways, especially as heir apparent to the throne of Great Britain. Frederick's decidedly laissez-faire attitude towards marriage, however, arose from a desire to obtain an additional allowance from Parliament to become financially independent of his father.

In a move that further gained his parents' ire, Prince Frederick continued to treat his new wife, Augusta, poorly. Augusta, who spoke little to no English, and who had no knowledge of Frederick's womanizing ways, was convinced by Frederick to accept his lover - Lady Archibald Hamilton - as one of her ladies of the bedchamber. Frederick did so by lying his new wife that there was no truth to rumors that Lady Hamilton was his mistress.

Frederick continued to abuse his position of power and title by manipulating his new wife, treating her in such a beastly manner that even his own mother, Queen Caroline, greatly pitied Augusta. All of these incidents made Queen Caroline, Frederick's mother, favor her second son - Prince William - for not only the succession of Hanover, but also succession to the British throne at the time.

Queen Caroline also stated of Augusta, Princess of Wales: "Poor creature, were she to spit in my face, I should only pity her for being under such a fool [Frederick]'s direction, and wipe it off."

When Augusta later gave birth to Prince George, Queen Caroline - his paternal grandmother - as well as his mother made sure that he was raised a "model Protestant prince". From an early age, Prince George was groomed to be the opposite of his father, being educated in secluded palaces by private tutors alongside his younger brother, Prince Edward, Duke of York and Albany.

On 31 March 1751, when Frederick unexpectedly died, the King showed little remorse for his son's death, and held a simple funeral.

Augusta, in turn, showed deference to King George II at Frederick's funeral, which pleased the King; and, as a result, Augusta was was named as a prospective regent by the King and Parliament. However, This caused a controversy and opposition from Prince William, Duke of Cumberland, who contested that he - and not Augusta - should be named regent.

The question is, could Prince William, Duke of Cumberland, arguably have sued for the succession?

Possibly; yet, by that time, he had become unpopular. While William is perhaps best known for defeating the Jacobite Rising at the Battle of Culloden in 1746, which made him immensely popular throughout Britain, he was opposed by the Tories, having been labelled "The Butcher of Culloden". William had ordered his troops to show no quarter against any Jacobite rebels, even going as far as to having soldiers kill wounded and dying Jacobite combatants after the battle. This was seen as a deeply abhorrent act, even by some of the officers serving under the Duke.

Additionally, Cumberland's own brother - Frederick, Prince of Wales - had also encouraged virulent attacks upon the Duke, presumably as retaliation for their parents favoring William, as opposed to Frederick.

This, coupled with William facing a heavy defeat at the Battle of Lauffeld on 2 July 1747, further contributed to the Duke's growing unpopularity. This greatly interfered with his success in politics; and, when Frederick, Prince of Wales died, William was unable to get the support to be named Regent, much less King. Instead, the regency was awarded to the the Dowager Princess of Wales - Augusta - who considered William to be her political enemy.

Aside from his advancing age and ill health, William, Duke of Cumberland had never quite recovered from his battlefield injuries; he was also morbidly obese. So, too, was William unmarried, preferring the company of several mistresses, while Prince George was the image of a devout, chaste Protestant prince looking for a bride. All of these factors made William pale as a candidate for the monarchy when compared to his young, healthy nephew,.

In a further blow to the Duke's chances to be named the next King, by 1757, further military losses by the Duke had seen the French overtake and occupy much of Hanover, and his army disbanded. Upon the Duke's return from his failed campaign to Britain, he had all but lost King George II's favor; the King is recorded as stating to him, "Here is my son, who has ruined me, and disgraced himself."

Having publicly humiliated himself and his father, William resigned all the military and public offices he held, and retired into private life, never again seeking to supplant the Dowager Princess of Wales - nor Prince George, his nephew.

The Duke of Cumberland would only live five years into King George III's reign, dying after a series of strokes at age 44; but, surprisingly, he had become one of King George III's most influential and trusted advisors. While William never became King himself, he helped to set up George III as King.

Bibliography

• Anderson, Fred (2000). Crucible of War: The Seven Years' War and the Fate of Empire in British North America, 1754-1766.

• Finch, Barbara Clay. Lives of the Princesses of Wales, Parts I-III.

• Neale, J. E. (1954) [1934], Queen Elizabeth I: A Biography (reprint ed.).

• Wilson, Derek (1981), Sweet Robin: A Biography of Robert Dudley Earl of Leicester 1533–1588.

• Van der Kiste, John (1997) George II and Queen Caroline.

• Et al.

This answer has been greatly edited down from its original format to meet Reddit's character limit.