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. We ask Allaah to exalt his mention as well as that of his family and all his companions.
First, you have to know that whenever a woman remarries, she is no longer entitled to foster her children (from the first husband). So the fostering of the children moves to whoever is appropriate and entitled to do so, like the father or the mother of the woman and the like. So you are not obliged to let this child live with you in your house and you can put a condition in the contract that he should not stay with his mother in your house. Then she will be obliged to fulfil this condition unless she is obliged to foster this child because no one else can do so, or whoever can foster him is not suitable to foster him.
Allaah knows best.