Is the khimar that covers the head and chest obligatory, and is it permissible to wear loose clothing over an ordinary short head covering, and what should I do if my mother refuses the khimar that covers the head and chest?

The legal hijab (definition) is not restricted to a specific outfit. Rather, it is obligatory that the conditions of the legal hijab are met, regardless of the outfit. The Muslim woman's dress is not exclusive to black, and she may wear any color if it covers her awrah (intimate parts), does not resemble men's clothing, is not tight exposing her limbs, is not transparent revealing what is beneath it, and is not a source of fitna (temptation). If the tarha (head covering) meets the conditions of the hijab, then it is permissible to wear it; otherwise, it is forbidden. Obedience to parents is in what is right. So, if the tarha fulfills the conditions of the hijab, then obey her. But if it does not, then it is not permissible for you to obey your mother in wearing it, because there is no obedience to a creature in disobedience to the Creator.