Is it permissible or forbidden for a mother to waive her share of the the house to her son, even if the rest of the siblings do not object?

The fundamental principle is the obligation for parents to be fair when giving gifts to their children. It is not permissible to favor one child over another unless there is a valid reason, such as a child having special needs, or being chronically ill, or blind, or having a large family, or being devoted to seeking knowledge. Alternatively, a gift may be withheld from some children due to their immorality or innovation (bid'ah). The mother is like the father in the obligation to equalize gifts among children. However, it is permissible for the mother to allocate her gift to one of her children and waive her right to her share of her husband's inheritance in favor of that child, provided that his siblings consent to it.