What is the ruling on shaking hands with non-mahram relatives and attending mixed-gender wedding parties in a country that does not apply Islamic Sharia, and is it obligatory to abandon these occasions despite the family's anger?

It is not permissible to shake hands with non-mahram individuals, even if they are relatives, based on the Prophet's (peace and blessings be upon him) saying: "For one of you to be stabbed in the head with an iron needle is better for him than to touch a woman who is not lawful for him." It is also not permissible to attend mixed-gender wedding parties, even if the attendees are relatives, due to his (peace and blessings be upon him) saying: "Beware of entering upon women," and his saying regarding the brother-in-law: "The brother-in-law is death." The forbidden mixing is that which is not regulated by Islamic guidelines. As for the mere presence of men and women in one place, along with adherence to hijab, avoidance of seclusion (khalwa), and lowering the gaze, it is not forbidden. One must reconcile between pleasing relatives and preserving the limits set by Allah. If there is a conflict, then displeasing people is easier than incurring Allah's wrath.