Am I obligated to obey my mother if she forbids me from visiting my sister, and is it permissible for me to disobey her if that results in her anger?

Obeying the mother in shunning the sister is not permissible, as it constitutes disobedience to the Creator. It is obligatory to maintain ties with the sister. If the mother insists on preventing it, then let the visit be discreet to avoid her displeasure. However, if the prevention is due to fear or a valid reason, then obedience to the mother is obligatory, without severing ties with the sister.