For 10 points, name this Duke of Lancaster, an advisor to Richard II whose eldest son became King Henry IV.
One of this man's daughters married the loser of the battle of Aljubarrota, King John I of Castile, after this man invaded Galicia at the head of a joint Anglo-Portuguese force in an effort to rule Castile himself. This man imprisoned Peter de la Mare at Nottingham Castle after the dissolution of the Good Parliament, then convened the Bad Parliament the next year to undo its reforms.  He had four children by his longtime mistress (*) Katherine Swynford. His support of the first-ever English poll tax led to the burning of his Savoy Palace during Wat Tyler's rebellion. He and his older brother Edward the Black Prince were sons of Edward III. For 10 points, name this Duke of Lancaster, an advisor to Richard II whose eldest son became King Henry IV.
One of this man's daughters married the loser of the battle of Aljubarrota, King John I of Castile, after this man invaded Galicia at the head of a joint Anglo-Portuguese force in an effort to rule Castile himself.
John of Gaunt, 1st Duke of Lancaster [prompt on John]