Is the husband sinful for refusing to pay alimony for his two daughters because the wife's father prevented her from returning to her husband after a dispute that occurred between her and the husband's sister, knowing that the husband had uttered a conditional divorce, stipulating her remaining in her family's home?

Your daughters' maintenance is obligatory upon you, and your wife's disobedience does not waive it. Thus, you would be sinful if you withheld it from them. As for your wife, she is not entitled to maintenance as long as she is disobedient by refusing to travel to you at her father's command, as he has no right to order her in this matter, and she must obey you. You may refer the matter to the judiciary to compel her father to release her, or you can attempt reconciliation with him through respected elders.