Is the death penalty for a man who killed his mother-in-law for inciting his daughter to prostitution legally valid?

A mother-in-law inciting her daughter to prostitution does not negate her status as a Muslim whose life is inviolable. Whoever intentionally kills a Muslim whose life is inviolable, without a just cause, shall be killed in retribution (qisas) unless his guardians pardon him, based on the Almighty's saying: ﴿O you who have believed, prescribed for you is legal retribution for those murdered — the free for the free, the slave for the slave, and the female for the female. But whoever is pardoned by his brother for something, then [pursue him] with good conduct and pay him [the compensation] with kindness. This is an alleviation from your Lord and a mercy. But whoever transgresses after that will have a painful punishment.﴾ [Al-Baqarah: 178], and His saying: ﴿And We ordained for them therein a life for a life, and an eye for an eye, and a nose for a nose, and an ear for an ear, and a tooth for a tooth, and for wounds is legal retribution. But whoever pardons [a right by way of charity] for it, it will be an expiation for him. And whoever does not judge by what Allah has revealed – then it is those who are the wrongdoers.﴾ [Al-Ma'idah: 45], and the saying of the Prophet (peace and blessings be upon him): "The shedding of the blood of a Muslim person is not permissible except in one of three cases: an adulterer who has been married, a life for a life, and one who abandons his religion and separates from the community." And the execution of a prescribed punishment (had) on whomever it is due is not the right of anyone except the ruler or his deputy, such as a judge.