Will I be sinful if I do not divorce my wife, whose father is holding her and has demanded that I divorce her, and will I have to pay the deferred mahr if I divorce her?

You are not obligated to divorce your wife merely because she or her father asks for a divorce without a valid reason. You are permitted to refuse the divorce until the woman forfeits her mahr (dowry) or a part of it, such as the deferred portion. However, if you divorce her without stipulating that she forfeit any part of her rights, then she is entitled to her entire mahr, both the immediate and deferred portions, and all other rights of a divorced woman.