All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
There are some conditions for the validity of the marriage contract the most important of which are the consent of the two spouses and the presence (and consent) of the guardian; you may read the other conditions in Fatwa 83629.
It appears that none of the two previous conditions were fulfilled in the marriage contract, so if this is the case, it is a void marriage and it must be invalidated. Hence, it is not permissible for that woman to go back to that man and it is not permissible for him to have sexual intercourse with her. However, the children should be traced back to their father if their mother was pregnant with them while the husband conducted the marriage contract with her even if the contract did not fulfill the conditions of the guardian and witnesses; this kind of contract is enough not to apply the Hadd of Zina (i.e. the corporal punishment determined by the Islamic Law for committing adultery/fornication) and enough for tracing the children back to their father.
On the other hand, it also appears that this girl is under the effect of magic and she acts without her will. However, it seems that this happened due to a mistake because how could she dare to travel in order to reside with a family far from her country while she has no relation with it at all. It is this carelessness about religion that brought about such bad consequences, so she should be careful in the future.