What should a husband do regarding his wife's daughter, who has started visiting her father and communicating with him daily, causing him distress and embarrassment, knowing that his wife is devout and fears for her daughter from her father's influence?

We do not know the reason for your preventing the girl from contacting her father. Her father has a right upon her that she should honor him, connect with him, and be good to him. You have the right to prevent her from contacting her father via your personal phone because it will cost you money, and you have the right not to spend on her. However, it is better that you continue to be good to her and that you do not prevent her from honoring her father and communicating with him, especially since he is a Muslim who is regular in his prayers. Your helping her to contact her father should be a cause for joy, as you are helping her in righteousness and piety.