He doesn't so much 'object' to her smiling in his face, as use the fact of her smiling as an occasion to warn her that he does not intend to be in any way faithful to her; remember the whole couplet: "Do not smile in my face, For I do not intend to stay long in this place". The 'don't' is more a way of saying, "You wouldn't smile like that if you knew me better, & what my plans for you are!"

~M~