Is there a sin upon the questioner if she refuses to return part of the money a man willingly gave her in exchange for her help in selling a piece of land, knowing that his son is demanding the return of part of the money, claiming that his father might have been mentally unsound due to old age?

If the agreement between the questioner and the landowner was for a known fee in exchange for her assistance in completing the sale, then there is no harm in that. This is considered either a ju'ala (commission) contract or an ijara (leasing/hiring) contract, both of which are permissible. There is no harm for the questioner in contenting herself with half of the agreed-upon amount and forgiving the man the other half. She is not obligated to return what she took to his son. And whoever claims that the father was not of sound mind must prove that in court.