Is it permissible for a mother to write over her house, which is all she owns, to her son, to the exclusion of her daughters, knowing that her daughters dislike him because he is not their full brother?

It is not permissible for a mother to transfer ownership of her house to one son to the exclusion of his siblings, unless there is a legitimate Sharia-compliant reason, such as that son being in need of housing while his siblings are not. In such a case, it is permissible to allow him to reside in it without transferring ownership to him. There is no harm in utilizing an asset to meet a need, provided that its ownership remains in the father's name. It is important to foster affection and love among siblings and maintain kinship ties.