If Henry VI's uncles were to produce heirs, preferrably males, then the succession question that basically dogged Henry until the birth of his son wouldn't arise. Two or three children each for John and Humphrey would have pushed York so far down the list that attempting to gain the crown would have been suicide, so now Yorkist rebellion.
Now the question becomes with whom and when do the royal uncles have children with?
John, a.k.a. Bedford, was regent of France for his nephew and married to Anne of Burgundy, the sister of Philip III of Burgundy. IOTL Anne died in December 1432 during childbirth, which led to Bedford marrying Jacquetta of Luxembourg. The Duke of Bedford's second marriage was politically disasterous as it angered his brother-in-law, who then signed a peace treaty with France which in turned helped the French in the war. Now let us say that Anne and her child, whether boy or girl, survive thus Bedford's second marriage doesn't happen. Bedford and Anne have two more children bringing their total up to three, with at least one being a male heir. The English-Burgundian alliance continues for a while longer at least thus helping to the English presence in France longer.
Humphrey, a.k.a. Gloucester, was regent of England for his nephew and was first married to Jacqueline, Countess of Holland, however her quarrel with Philip III resulted in an annualment and Gloucester married his mistress Eleanor Cobham, who was tried and convict of witchcraft against the King (though Gloucester's enemies might have had something to do with that). Gloucester and Jacqueline had a stillborn child in 1424 and with Eleanor he had no children. But to illegitimate offspring were a son named Arthur (d. 1447) and a daughter named Antigone who married the 2nd Earl of Tankerville. So let's say Gloucester's stillborn child in 1424 lives and its a boy, who he raises while seperated from Jacqueline until she dies in 1432.
Thus you have besides Henry VI, at least two other male grandchildren of Henry IV. Also as a result of this, Bedford probably doesn't die in 1435 while negoitating the Treat of Arras, which ended the English-Burgundian alliance by making peace between France and Burgundy. Thus Bedford continues supporting the war and giving Humphrey political help in England against the Peace Party headed by Henry Beaufort.
When Henry VI assumed the reins of government in 1437, both of his uncles are alive and able to advise him and considering they have male heirs of their own at this time the efforts of Henry Beaufort are blunted. With Henry VI's foreign policy not firmly in the peace party, the marriage to Maragret of Anjou doesn't occur. And the butterflies just start appearing all over the place...