Actually, Edward III had three children who died in infancy : the two you mentionned, William of Hatfield (1337) and William of Windsor (1348), but also a third child, Thomas of Windsor (1347).
Only William of Hatfield's survival would make a significant change in History though. If everything goes as OTL and the Black Prince and his eldest son Edward of Angoulême (1365-1372) die on Schedule, then when Richard II will ascends the throne at age 10, his heir will be William of Hatfield (he would 40 in 1377, so there is a chance he would be still alive) or one of William's children (it is very likely that there would be one).
This fact can butterfly away the Roses War as William of Hatfield is older than Lionel of Clarence, John of Gaunt and Edmund of Langley from whom descend both the Lancasters (via John of Gaunt) and the Yorks (who descend both from Lionel of Clarence and Edmund of Langley).
Unless William's line turns out to be exclusively female, his sons are likely to become the next in line after Richard II and Henry Bolingbroke's position will be weaker than OTL.
And even if William's line turned out to be exclusively female, this would change the Roses War in itself: the Lancasters would still be one of the two sides fighting, but the other wouldn't forcibly be the Yorks but descendants of William.
Also, an interesting fact would be that William would be 40 when Richard II is crowned King at age 10. If William is a very ambitious guy, it is highly possible that he tries to snatch the crown for himself.