...So what im really saying here is what right did both the yorks and the lancasters really have...
I'm not sure what's confusing you here.
Richard II was the king. He was king because his father, Edward the Black Prince, was the eldest son of the previous king, Edward III. Richard didn't have any children, so his heir presumptive was the next male in the line of succession - the grandson of his father's eldest brother,
Roger Mortimer, then later Roger's son,
Edmund. The eldest son of his father's second brother, Henry of Bolingbroke, conflicted with
Richard lead a rising and seized the throne, putting himself on it as
Henry IV.
Go forward in time a bit and Roger's grandson,
Richard, Duke of York, conflicted with
Henry VI and pointed out that hey, his bloodline was of a senior line to the king's, so really he should be king. He lead a rising and when he was killed his sons continued that rising until eventually winning (twice) and establishing the eldest,
Edward IV, on the throne.
People usurping the throne happened before, and happened again, but the case of the Lancasters/Yorks is one of the few ones where a house with a better claim was able to restore itself. Other usurpations/conquests happened under:
- William the Conqueror, who conquered England from Harald Godwinson
- Henry I, who seized the throne on the death of his elder brother, William II, over his elder brother Robert Curthose
- Stephen, who seized the throne over his female cousin, Matilda. Matilda's father, Henry I, had no male heirs so made the nobles swear to support his daughter as the heir, however when he died his nephew (the eldest son of his sister, and closest male relation) put himself on the throne, leading to a period of time known as the Anarchy as the two cousins fought for control. In the end, Stephen agreed to name Matilda's son as his heir, resulting in Henry II becoming king
- Edward III's supporters, lead by his mother, overthrew his father, Edward II
- Richard II's cousin, Henry IV, overthrew him. Later, Henry's grandson, Henry VI, would be overthrown by the great-grandson of Richard's heir presumptive, Edward IV
- Richard III usurped the throne of his nephew, Edward V
- Henry VII conquered the throne from Richard III. Both he and his son, Henry VIII, would put down Yorkist risings throughout their reigns
- Jane Grey attempted to usurp her cousin, Mary I, on the death of Mary's half-brother, Edward VI, but would be overthrown very quickly and eventually executed
- Similarly, during the reign of Mary's sister, Elizabeth II, their other cousin, Mary of Scots, was the subject of an attempt to usurp the throne, leading to Mary's execution
- Charles I was overthrown by Parliament and Oliver Cromwell. After Cromwell's death his son, Richard, became Lord Protector briefly before resigning in favour of the restoration of the monarchy under Charles' elder son, Charles II
- James II was also overthrown by Parliament in favour of his daughter, Mary II, and her husband, William III. On William's death, Mary's sister, Anne, became monarch, and on her death George I, was asked to be monarch, over the 50+ people that came before him in the line of succession but were deemed undesirable
- Edward VIII was pushed off the throne by Parliament and the Church because the woman he wanted to marry was deemed undesirable. His eldest brother, George VI, became monarch