Is my absence from my cousins' weddings considered a shortcoming on my part in maintaining kinship ties, especially given that these are women's weddings where dancing and singing take place?

Whoever is invited to a wedding banquet, it is obligatory for him to attend, based on the Hadith of the Prophet, peace and blessings be upon him. The obligation is waived if there is an objectionable act that the invitee cannot change. If there are no objectionable acts and you fail to attend, you have committed a Sharia violation, unless you were not invited. As for attending the weddings of relatives and maintaining ties of kinship, the matter is subject to custom. If failing to attend is considered a severance of ties, then attendance is obligatory, unless there are Sharia violations.