The issue seems to be more about ‘who has got the control’ than the duppata. Duppatta seems to be just an indication of who wears the pants in the house. Duppatta and pants don’t go together by the way.
Anyways, one of you will have to bend and whoever bends will hear it from the crowd but it may avoid resentment. Couple who don’t work towards the big picture normally f up their lives.