If you start looking at problems with the succession to the English crown, there are many, many examples of problematic and disputed successions. There’s no end to it. Succession comes down to power and politics. It always has, and the rules of succession (such as they were) were changed from time to time.
Today it doesn’t matter so much because the monarch is not an absolute ruler, but in the past it did matter, and decisions were almost always made for practical and political reasons. The rules were just guidelines.
A very brief summary of problems with the succession to the English throne:
William the Conqueror invaded and took over the country by force. Does this mean that all English monarchs since 1066 have had no right to the throne? Should we go back and try to find the closest living relative of the Saxon kings? The House of Wessex had a system whereby a council decided who the next king should be, and they could choose anyone. Harold Godwinson wasn’t even a blood relative of Edward the Confessor, who died early in 1066. However, there were plenty of wars and succession disputes among the various Saxon kingdoms before the House of Wessex gained control, so who was the valid ruler? Should we go back to the ancient Britons before the Roman occupation when there were numerous tribal leaders and tribal conflicts?
After the Norman conquest, Henry I defeated his older brother Robert in battle and imprisoned him for life. Does that mean no future monarchs had a right to throne? The succession of Henry I’s daughter Matilda was disputed because many Norman barons felt that the Salic law prohibiting women succeeding to the throne should apply in England. After a civil war, Henry I’s nephew Stephen became king. But Matilda’s son, Henry Plantagenet, forced Stephen to nominate him as his successor, in place of Stephen’s own son. How valid was that?
Henry II tried to start a convention of crowning a successor in own lifetime, and his son Henry was crowned as the ‘Young King’, but it didn’t work out. When Henry II died, the question was whether Arthur, the infant son of Geoffrey, Duke of Brittany, had a better right to throne than Richard, the younger brother of Geoffrey. According to Norman law Richard had the better right, but according to the law of Anjou Arthur had the better right. (The Plantagenets were descended in the male line from Geoffrey, Count of Anjou.) Richard the Lionheart became king, then his younger brother John. John still considered Arthur of Brittany’s claim to be a threat to him, and had him imprisoned and murdered.
An identical situation arose on the death of Edward III, but this time the decision went the other way, and Richard II, the son of the deceased older brother, became king, not John of Gaunt, Duke of Lancaster, the next surviving son of Edward III.
Richard II was overthrown in a coup, and Henry IV, the son of John of Gaunt, became king with the full consent and support of Parliament and the Church, even though it could be argued that Edward Mortimer the descendent of Lionel of Antwerp had a better claim. Mortimer himself gave up his claim, and was loyal to the House of Lancaster, but the House of York inherited his claim via Mortimer’s sister. The House of York supported and swore loyalty to Henry IV, Henry V, and Henry VI, until political issues resulted in them reviving their claim. The Yorkists gained power in a series of civil wars, and murdered Henry VI. Richard III made the claim mentioned by the OP as a pretext to justify seizing the throne by force, and murdered his nephews, Edward IV’s sons. (No, I don’t want to argue with fanatical supporters of Richard III.)
The Tudors came to the throne by a political compromise which had little basis in theoretical claims to the throne. After the Reformation, religious issues became a major factor.
Everyone agreed that Edward VI should succeed Henry VIII, on the principle of male primogeniture (a younger male takes precedence over older females - this has now been changed in the 21st century) but after that, there were different opinions. Catholics felt that Henry’s marriage to Catherine of Aragon was valid and their daughter Mary was legitimate, but his marriage to Anne Boleyn was invalid, so Elizabeth was illegitimate. Hardline Protestants felt that Henry’s marriage to Catherine of Aragon was never valid in the first place, because it was only made possible by a special dispensation of the Pope, so Mary was illegitimate and Elizabeth was legitimate. Moderate Protestants felt that both were legitimate. However, by Edward VI’s Devise for the Succession, both were declared illegitimate. Take your pick.
In the mid to late 16th century it was said that if you asked 10 people about the succession to throne, you would get 10 different opinions.
In the next century, James II was overthrown in the Glorious Revolution, and the Act of Succession of 1701 banned Catholics from the throne. So on the death of Queen Anne, all Catholics in line for the throne were ignored, and George I became king. Nearly 60 years of Jacobite uprisings after the Glorious Revolution failed to restore the House of Stuart. Catholics are still banned from the throne to this day.
In the 18th century, a constitutional monarchy was introduced, and then it didn’t matter so much who was king or queen, so it became less a matter of contention.