Historically she died of plague in 1395, without the couple having any children. But what if she survived, and produced a son somewhere along the way? Let's call him Edward. He would be of an age for Isabella to marry the Prince of Wales for starters.
Isabella seems like a racing certainty, if Richard survives long enough to wed off his son. (See below re: Lords Appellant.) Richard was obsessed with France and -- unless the birth of an English heir somehow butterflies away Charles VI's breakdown -- the French were desperate for peace by the 1390s.
Anne was said to have had a moderating influence on Richard; perhaps a living son and wife mellows him somewhat, and the murder of Gloucester and Arundel doesn't happen.
Might her survival butterfly the Revenge Parliament?
Thing is, iotl Richard took the Lords Appellants' destruction of his government personally (can't blame him lol), so I think Gloucester and Arundel are still toast, regardless of Anne's moderating influence.
Anne was known as having a "moderating influence," but this refers as much (or more) to her moderating the
political community as it does Richard himself. Anne was the figure to whom lords most often brought disputes because the great lords of the realm did not trust Richard to be fair or impartial in his dealings with them.
I think the overstatement of her "moderating influence" on Richard himself is most clear in the fact that he continued to reign without incident and government remained stable for two years after her death. It is not until the marriage to Isabella that the wheels begin to come off. Richard had sought assurances from the French during marriage negotiations that they would support him in a civil war against his own magnates. That he has his revenge so quickly thereafter suggests to me that security the French alliance brought him was a much greater factor in Richard's tyranny than Anne's death and that stories of him becoming mentally unspooled by her death are exaggerated. (This, of course, is not to say that her death had
no effect on him.)
Regardless, even if Bolongbroke ends up deposing Richard, I would think that he would not be able to depose his nephew; my gut says Henry would be content, at least initially, to play the role of his father John of Gaunt, and become the eminence grise behind his underaged nephew's throne.
Depending on when the child is born, I think Bolingbroke's 1399 campaign may be butterflied away entirely because -- if Richard had a son in the mid-1380s, as
@Kellan Sullivan suggests as one possible date for the boy's birth -- then Bolingbroke's objection to Gloucester deposing Richard in 1387-88 disappears entirely, and Richard may be removed or killed at that time.
Bolingbroke is known to have opposed deposing Richard in OTL 1387-88 for fear that Gloucester would claim the crown for himself, as Bolingbroke's father was out of the country at the time. In an ATL where there is a young prince around, the Lords Appellant -- Bolingbroke included -- may rebel with the intention of removing Richard, putting the young prince on the throne, and governing the realm in his name. To put it simply, Richard is probably dead 12 years earlier in an ATL where he has a son in 1386.
And, of course, without the Bolingbroke usurpation you don't see Glyndwr and perhaps not Percy (as that was largely related).
Wales was going to revolt. It was only a matter of time. The English had been remarkably hard on the Welsh in the decades since the Black Death. The level of resentment toward the local English gentry and the marcher lords was extreme. The place was a powderkeg ready to explode. In OTL, the dispute between Grey and Glydnwr was the match that lit the blue touch paper, but it would only have been a matter of time before
some local dispute did the same thing in ATL.
Yeah, a lot of the complaints against Richard come across as aristocratic bickering, though he certainly didn't help his case.
This is a remarkably pro-Ricardian take on the events of his reign