What is required of me to fulfill my duty as a daughter, and what is the ruling on shunning or avoiding my mother to preserve my home and husband?

What you are experiencing is good evidence of the danger of divorce and its impact on children. Spouses must care for their children, look after their affairs, and guide them well. The father and mother remain worthy of piety and benevolence, because Allah has made it obligatory to honor one's parents, even if they are disbelievers, so what if they are Muslims? Children must treat their parents kindly and maintain ties with them. This is done through what is customarily accepted, such as calling and checking on them, giving gifts, and everything that is conventionally considered maintaining ties.