Is the questioner considered a dayyūth for being unable to prevent his mother from intermingling with non-mahrams and uncovering her face? And is his mother's uncovering her face during travel due to her illness forbidden, or is it permissible for her?

A mother who is lenient in intermingling with foreign men, speaking with them, and uncovering her face before them, is committing reprehensible acts. Continue to advise her kindly, because enjoining good and forbidding evil with parents is not like with others. She has no excuse for being embarrassed by people, and if her husband condones this, he is a cuckold (dayyūth). Covering the face is obligatory, and shortness of breath is not an excuse for uncovering it. She should let down over her face what covers it without discomfort. If she is unable to do so, she may uncover it out of necessity, and she must avoid being in the presence of foreign men except when necessary.