Is it permissible for the mother and siblings to nullify an agreement made between them and one of the sons, even though there are no witnesses or written proofs, and Allah is the only witness to this agreement?

We do not know the true nature of the agreement that was made, to determine whether it is binding or not. If the agreement was merely a promise, then fulfilling it is commendable (mustahabb) and not obligatory (wajib (definition)) according to the majority of scholars, and it is permissible not to fulfill it unless that causes harm to the promised party, except in the case of an excuse. However, if it was a binding contract, such as a sale or a lease, then its pillars (arkān) and conditions (shurūt) must be met, and the delay or lack of formal documentation does not affect its validity.