Is it obligatory to advise one's mother even if she gets angry at the advice and drives away the advisor? Does her anger nullify the obligation to admonish her? And how can one deal with her and with others through exhortation?

"Calling to Allah is one of the best acts of worship and is obligatory upon every Muslim according to their knowledge and ability. What you are doing by inviting your relatives to Islam is a great act of obedience. Your mother is not permitted to forbid you from this, and you must be patient with her and meet her actions with forgiveness and good character; perhaps that will influence her. The right of a mother is great, and whatever ill-treatment she may exhibit, meet it with patience and kindness. Do not let her anger deter you from calling to Allah with wisdom and good admonition, and forbidding evil in a gentle manner, especially if it becomes necessary for you to do so. If there is someone else performing Da'wah (calling to Allah) besides you, then there is no harm in refraining from it in obedience to your mother, as it is a collective obligation (fard kifaya). You can utilize times when your mother is not present or is busy for Da'wah. Increase your supplications for her guidance. If she does something that contradicts Islamic law, advise her gently when she is calm and pleased, and it is not permissible to rebuke her or be harsh with her. The mentioned Hadith ('The Prophet, peace and blessings of Allah be upon him, used to choose opportune times for us to admonish us, for fear of causing us weariness') means observing appropriate times for reminding to avoid boredom. Calling to Allah requires effort and patience."