Is a daughter's refusal to accompany her mother to offer condolences to a relative considered a shortcoming in her duty towards her mother, and is the mother's anger and disregard for her daughter considered an overreaction?

There is no objection to politely excusing yourself to your mother from accompanying her to a condolence gathering. However, if she does not accept your excuse and becomes angry, then it is obligatory for you to obey her if there is no harm to you in accompanying her and if your mother has a valid purpose, even if it involves tolerable hardship. You must repent to Allah, seek your mother's forgiveness, appease her, and strive to be dutiful to her, for the right of the mother is immense, and obeying her in what is good is among the most emphasized obligations. Your mother should accept your excuse.