Is it permissible for a wife to stipulate in her will that her husband not marry after her death, in the house she gifted to her children, knowing that the husband does not own a home and wishes to marry, and the children want to keep their father in the house? Should this stipulation be honored or disregarded, and would disregarding it burden the children with sin?

A wife should not instruct her children not to allow their father to marry in her house, as this is an unbeneficial instruction. If the wife genuinely gifted her house to her children, then they own it, and they have the right to dispose of it and to allow their father to stay with them and marry in it. If the mother instructed that the husband should not be allowed to marry in this house, then this instruction is not binding, and there is no sin upon the children if they disobey it, because fulfilling the covenants of parents after their death applies only to what is obligatory or recommended.