Am I obligated to listen to my mother and treat my sister normally after she appeared in immodest attire at her engagement party, or would I thereby be assisting in disobedience, or should I side with my father, who is still angry with her?

If a sister wears a tight dress and uncovers her hair in front of non-mahram men, she has committed something forbidden, and she must be advised against it. If she repents and regrets, then she should not be shunned; rather, ties with her must be maintained, and the mother must be obeyed, for one who repents from a sin is like one who has no sin. However, if she insists on disobedience, then it is obligatory to advise her and explain the Shar'i ruling. Shunning her is not necessary unless shunning is a means to deter her from the evil.