Am I sinful if I do not give my father the dowry for the woman he wishes to marry, knowing that he is old and her reputation is not good?

The jurists have obligated the maintenance of poor parents upon their child. The questioner's father is in need, so his maintenance is obligatory upon him. The Prophet, peace and blessings be upon him, said: "You and your wealth belong to your father." Marriage is a need, so the questioner should honor his father by facilitating it for him. There is no religious impediment to the father marrying a young or divorced woman, as long as she is not known for indecency. Perhaps her marriage to this man will reform her.