What would be Henry's sister's (Mary?) fate and how would her existence affect situation of House of Lancaster? As royal daughter *Mary* is too high born for domestic match,
One possible exception. Henry VI was very close friends with Henry Beauchamp, 14th Earl and First (and only) Duke of Warwick, with whom he had been brought up, and whomm he showered with titles. He might have been i with a chance, though it would have ruffled a few feathers. .
In that event, the really big question is whether Beauchamp's early death in 1446 is butterflied away. If he lives, then Richard Neville (OTL's "Kingmaker") remains just a minor baron.