Does the mother's share of the father's inheritance rightfully become the property of her seven children after her death, and is it permissible for her to disinherit some of the children from this share while she is alive?

A mother's bequest to some of her children to the exclusion of others is invalid, for all that she leaves behind after her death is considered an inheritance for all her heirs, including her disobedient children. The disobedience of children does not prevent them from inheriting. As for a gift made during one's lifetime, it is permissible to prefer some children over others if there is a legitimate Sharia (definition) reason for doing so.