Is a sister bound by an oath she swore under duress, and what is her sin if she does what she swore not to do while coerced, and is an expiation for the oath incumbent upon her?

An oath sworn under duress and coercion is not binding, and no expiation (kaffara) is required for it. This is because one of the conditions for expiation to be obligatory is that the one swearing the oath must do so voluntarily. This is based on Allah's saying: "Whoever disbelieves in Allah after his belief - except for one who is forced [to recant] while his heart is secure in faith" (Quran 16:106), and on the Prophet's (peace be upon him) saying: "My Ummah has been forgiven for mistakes, forgetfulness, and what they are coerced into."