So got two questions here:
Firstly, what might the consequences be if Margaret Beaufort, mother of Henry VII had had a brother? Now, if she has a brother, likely named Henry for the King at the time, the boy would be Duke of Somerset, who would be given his wardenship should his father still off himself because of depression/failures in France? How does this influence the development of the War of the Roses, and the Beaufort-York rivalry, with Edmund Beaufort not holding the Duchy of Somerset? Who might this boy, let's call him Henry Beaufort, 2nd Duke of Somerset marry? What role might he play in government?
Secondly: What might change had Edmund Beaufort, 2nd/1st Duke of Somerset, not died at the battle of St Albans? If he had instead lived through that, through loveday etc? Would things have gotten worse for the Yorkists?