One error that always rips me right out of a story is the idea that a Regency era peer can pick someone to succeed him — disinherit one son and promote another, pass the title on to an illegitimate son, or repudiate a son who has been accepted as his own.
Who succeeds to a peerage is set out in the documents that established the peerage. In most cases, the wording is “heirs male of the body”. What that means is the peer’s oldest surviving legitimate son inherits the peerage.
And by eldest legitimate son, we mean the eldest son born within the marriage. If the peer has three sons by his mistress and then marries her and has a fourth, the fourth son inherits. The other three are not legitimate. If the eldest surviving boy born within the marriage was the result of the wife having an affair with another man, but the peer accepts the boy as his own, then that the boy is the eldest legitimate son.
And he pretty much had to accept the boy as his own. The law assumed that any child born within a marriage was the child of the husband, unless the father could prove otherwise. That was not simply a matter of denying responsibility, he had to produce evidence that the child could not be his; for example, that he was in another country for the entire period in which conception was possible.
Both men marrying their mistresses and sons of other fathers inherited in real life and the same circumstances are found in Regency fiction.
The peer has no choice about this. He can refuse to leave the heir any property that is not entailed to the title, he can run the entailed property down so that it isn’t worth anything, he can throw the heir out of the house and not speak to him for the reminder of his own life. But once he dies, the heir gets the title (and any entailed lands).