What is the ruling on a husband gifting a house to his second wife, after her request and insistence, and after his death it became apparent that the gift was in secret, with the knowledge of the second wife and her son, and in the presence of children from a deceased wife and one son from the second wife?

The Sharia courts are the primary authority for settling disputes. For a gift (hiba) to be valid, it must not be made during a life-threatening illness, and the wife must take full possession of it. A claim of a gift is not accepted except with proof, and the existence of children from another wife or the non-declaration of the gift until after a period of its validity does not prevent its acceptance. The important thing is its proven existence and full possession.