Is it permissible to force a Kitabiyyah wife—who is hostile towards Islam and threatens not to raise the children upon the religion—to have an abortion, or to give her medication for that without her knowledge, taking into account not to harm her, especially since the marriage is not registered and the husband has no rights in her country?

Aborting the fetus is not permissible; abortion is forbidden at any stage of its development, and fear for the child's religion does not make it permissible. The child might not live, or his mother might embrace Islam. If the child survives and his mother remains a disbeliever, you are responsible for his upbringing and his religion. If a divorce occurs, the disbelieving mother has no right to custody; because one of the conditions for custody, according to the preponderant opinion, is Islam. Marriage to a woman of the People of the Book is disliked due to these matters.