Is it permissible for a mother to revoke a gift she made to her children nineteen years ago? And does her demand for them to return the house constitute a will that is obligatory to execute according to Sharia? And what is the Sharia ruling on a father's written will?

The division of your father's inheritance that took place is binding and cannot be revoked, as long as everyone was adult, of sound mind, and initially agreed to it, unless the share of the mentally disabled sister was less than what she is legally entitled to, in which case she must be given her full right. As for your mother retracting her gift (hiba), she may do so under certain conditions, including that the children have not disposed of it by transfer or alteration, or that a life-threatening illness has afflicted the giver or the recipient. The mother must also treat all her children equally in gifts.