Regarding Maud after Stephen’s defeat: she really didn’t have any power but essentially abdicated in favor of her son, Henry II, who was- as you probably already know- well up to the task of ruling. Any influence she had with him had been largely usurped by the time he was crowned by her new daughter-in-law, the Queen Mother of Cougars, Eleanor of Aquitaine.
While the movie didn’t really have time to deal with Henry’s complicated succession and, understandably for dramatic purposes, made it quick, it was actually settled more by diplomacy than by sword. As in the miniseries Stephen really did adore his son Eustace, though unlike in the miniseries Eustace wasn’t Earl of NambyPambyland but a spoiled little bastard with a nasty reputation; when he died it was not on the battlefield as but it really did devastate his father as much as it in the miniseries, but there were many people who were quite happy about it including on Team Stephen because the thoughts of King Eustace were terrifying to them. (Among this group: Eustace’s brother William, who was never that loved by their father.) There is suspicion dating to not long after his death that Eustace was done in by members of Team Stephen who were either bribed by Team Henry or just wanted “peace, dammit, peace”.
In any case, Stephen was already devastated by the death of his wife, Matilda of Boulougne, who was unfortunately not in the miniseries but was a real piece of work herself; when he was captured she was his regent and a kickass one at that. (It can get very confusing remembering which Maud/Matilda you’re dealing with, especially since they were both Queen of England at some point or other, so they’re usually delineated as “the Empress” or “the Countess”.) Eustace’s death very soon after Maud’s basically made him give up the ghost. He was getting old (late 50s in an era without any of the modern treatments for the aches and pains of middle age), he was sick to death of fighting, he knew that Henry was young and eager to fight and had just married the richest woman in Europe as well (though only because his younger brother failed to kidnap her on the way to her wedding) while he himself just wants to die in peace. HOWEVER, he still had plenty of soldiers and could have kept up the war for years more at least.
So instead he hammered out the Treaty of Winchester:
1- Stephen got to remain king until his natural death
2- Upon his death Henry would be the clear king
3- Maud relinquishes any claims to Henry
4- Stephen’s considerable holdings in France and his English estates would be split between his other children
5- Several castles that were constructed and titles created by both sides during The Anarchy would be done away with and most titles and estates would go back to status quo antebellum (the way they were before the war)
6- A general amnesty for those who fought on both sides, with only a few very glaring exceptions
So since Richard was the rightful heir to the Earl of Shiring before the war, he’d have been restored and his killing of Gloucester (who of course wasn’t really killed by Richard since Gloucester was real and Rich wasn’t, plus Gloucester didn’t die in battle) was overlooked. True, were it real Maud would likely have found a way to poison him in his sleep, but Henry was a new and young king who wanted peace because war is bloody expensive and he wanted to fight the King of France more than he wanted to fight in England. His French possessions, which at their height were greater than those held by the King of France, were his real darlings and his real moneymakers and while he certainly took a very active interest in English affairs he was more inclined to let it be his cash cow to bolster up his adventures on the Continent (though he did love having the title of King and Eleanor liked being a Queen again).
In real life, incidentally, Richard would most likely have still been the Earl of Shiring after his father’s execution; it was extremely rare for a family’s titles and lands to be taken even if the last holder was a traitor. The Tudors would do things like that a lot more, but the Plantaganets not so much and it was quite common for your best friend to be the grandson or nephew of a guy your uncle or grandpa beheaded. King John would also become notorious for selling the guardianships of orphaned heirs and the hands-in-marriage of orphaned heiresses (he even sold his ex-wife in remarriage).
PS- Link to an older post detailing some of the reasons I didn’t like the book