Is the brother's wife entitled to object to the amicable distribution of the inheritance among the heirs, and to demand possession of one of the two houses under the pretext that they lived in it before the mother's death?

If the heirs are adult and of sound mind, there is no objection to them agreeing on the division of the inheritance. The son's wife has no right to object because she is not among the heirs. The house the son lives in is considered part of the inheritance, and he has no right to monopolize it merely because he lives in it, just as his wife has no right to claim the house. If a dispute arises among the heirs, the matter should be referred to the Sharia (definition) court.