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.
If this divorce is a revocable divorce and you are still in your waiting period from this divorce, then you are still considered as a wife and it is permissible for you to live in the same house with your husband who divorced you and you are not obliged to wear Hijab in front of him, according to the view of some scholars . However, if the divorce is irrevocable or that it is a revocable divorce but the waiting period has expired, then you are a marriageable woman to him, in which case it is not permissible for you to live with him in the same house where you share its amenities with him, like the kitchen, toilets, hall, and have only one main door into the apartment. Your desire for the children not to know that you and your husband are divorced is not a sound reason for you to live with him in the same house or not to wear Hijab in front of him. However, if each one of you has his own and separate amenities, and entrance then it is permissible. If reconciliation is possible, you should endeavour for it in order to avoid any embarrassment and to achieve a benefit for your children.
For more benefit, please refer to Fatwa 90016.
Allaah Knows best.