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.
The guardian of the girl- who is the brother in this case- is not permitted to condition the person who proposed to marry his sister to inform his mother and family about this marriage unless he knows, by some indications, that if the husband does not inform his family about this marriage, this will cause problems for his sister which she will not be able to bear. So, if he is pretty sure that this is the case, then he is allowed to condition that, but this condition should not be included in the contract, and it does not make what is forbidden lawful, or renders what is lawful forbidden.
Since this man is married and has children, it might be that his family prevents him from marrying a second wife, and this will cause problems for the sister whom he proposed to. So, this condition might help prevent some problems which might arise by him marrying a second wife, especially if he is living with his family.
Allaah Knows best.