What is the ruling on participating in relatives' celebrations after Ishā' (night prayer), where participants exchange worldly conversations, given the Prophet's - may Allah's peace and blessings be upon him - dislike for talking about worldly matters after Ishā'?

There is no harm in attending social events for relatives or others, as long as they do not include any forbidden acts, or lead to missing the Fajr prayer. Such attendance strengthens ties and increases affection. As for the disapproval of speaking after Isha, it is specific to cases where the conversation is not for a desired matter, a need, or a good purpose, such as reading Hadith, studying jurisprudence, or conversing with a guest. All of these are not disliked.