Is it permissible for a brother to take the price difference of a mobile phone from his sister, who sold it for less than its value, after he had bought the phone for her at the request of her husband's mother, and they delayed in paying the amount, which caused her problems with her husband?

You made a mistake by taking the mobile phone back and selling it for less than its value. Your brother should demand the full price of his mobile phone from your husband's mother, not from you, because she is the one who bought the mobile phone from him, and you were not acting as her agent. You are responsible to your husband's mother for the phone you sold without her permission, and she is responsible to your brother for the price of his phone. It is advisable to reconcile and reach an agreement among yourselves. Perhaps your brother will forgive if the mistake is acknowledged to him.