Is it permissible for a woman to ride in a taxi alone with her young children for a distance of 10 kilometers, and is the husband justified in becoming angry at this action if he had previously warned her against riding in a taxi without her brother?

Being alone (khalwa) between a woman and a driver is impermissible. Young children do not prevent this impermissibility. The husband has the right to be angry out of protective jealousy for his religion and honor. Whoever is not protective of his honor is a cuckold (dayyuth). It is not permissible for a woman to leave her husband's house except with his permission.