Is it permissible for a son to prevent his elderly mother, who is in need of care, from traveling with a Mahram to her daughter, knowing that she is suffering from difficult circumstances in her country?

Your brother has no authority over his mother such that he can prevent her from traveling, especially since she has a mahram accompanying her and your husband agrees to her staying with you. Preventing her from traveling in this case is a form of undutifulness. He must fear Allah and repent to Him, and not stand between his mother and her well-being. You can seek the help of some virtuous people to advise him.