Is it permissible to propose to a girl whose father died while objecting to marrying her, and the mother currently refuses on the pretext of the father's displeasure?

You must satisfy your mother by marrying the girl she has chosen for you, and this is considered an act of righteousness towards her. However, if you love another girl, try to convince your mother to let you marry her, unless she has an acceptable justification for her rejection. If she has a valid reason, then seek someone else, and Allah will compensate you with someone better.