Is it permissible for a man to sleep in the same house as his divorced wife in order to visit the children?

A woman who is revocably divorced (talaq raj'i) is like a wife before her waiting period ('iddah) expires; her husband may seclude himself with her. As for a woman who is irrevocably divorced (talaq ba'in), she is a stranger to the husband. It is not permissible for him to seclude himself with her or to live with her in the same house, except out of necessity and provided there is no fear of temptation (fitnah), on condition that she has a separate section with her own facilities.