A married man married a widow as a second wife in the presence of her family and relatives. The condition he set for her was that she not bear any children, since he has ten children from his first wife and because he is elderly (53 years old).  His second condition was that neither of them inherit from the other. This condition was set in exchange of his purchasing a house in her name. This house, and anything he buys for her, is considered in lieu of any inheritance from him.

He does not lead a happy marital life with his first wife. The second is a divorcee who desires security and stability, and a husband who will support her financially.

Each condition was met with her consent, both in the marriage contract and before the witnesses, her guardian, and her relatives. It is important to note that she willingly consented to these conditions while she was of sane mind. We kindly request your guidance, and may Allah grans you the best reward on our behalf.

If the case is as stated in the question, that the marriage contract fulfills all the required conditions and pillars of a marriage contract, then the contract itself is valid. However, the two conditions are invalid because they contradict the essential elements of the marriage contract. If the wife agrees to not having children due to the special circumstances that prompted her to do so, and she is content with this agreement, then there is no objection to her using contraception to prevent pregnancy. The property that the husband gave to her is considered a gift and does not forfeit the Islamic legal inheritance rights of either party.

And Allah Almighty knows best.