What is the ruling on the relationship between a woman who embraced Islam, married, and had children in another country, after she had abandoned her family and homeland before her conversion to Islam, and had no contact with them? Do her family have any right over her?

A Muslim's emigration from a disbelieving people is obligatory if they fear for their religion. So, if a woman emigrates fearing for her religion, she has fulfilled her obligation. It is permissible for her to marry a Muslim with a guardian from the judge or the Muslim community. If her visit to her disbelieving family causes a trial in her religion, then she should not visit them. Otherwise, there is no harm in maintaining ties with them, and she must treat them kindly.