How should a Muslim woman deal with her non-Muslim family members who do not accept her دعوتها (invitation to Islam), and should she continue to maintain ties of kinship with them or limit her relationship with them?

A Muslim should take the initiative to invite their non-Muslim family members to Islam, as they are the most deserving of his invitation. He should pursue every permissible means to do so, such as offering books and tapes, hosting influential figures, and drawing closer to them through gifts, good treatment, excellent manners, avoiding harshness, and persistently praying to Allah for their guidance. Allah Almighty has commanded kindness towards disbelieving parents, while not obeying them in associating partners with Allah, as stated in His verse: (But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them but accompany them in [this] world with appropriate kindness and follow the way of those who turn back to Me).