A parent is not killed in Qisas (retaliation) for their offspring according to the Shafi, Hanafi and Hanbali schools of thought.
Instead Diyya (blood-money) is taken from the killer and given to the remaining heirs of killed person.
رجل من بني مدلج قتل ابنه فأخذ منه عمر مائة من الإبل ثلاثين حقة وثلاثين جذعة وأربعين خلفة فقال ابن أخي المقتول سمعت رسول ...
No, a person can not seek Qisas from their parent (father or mother), and only Diyyah, Tazir and Kaffarah would apply.
The evidence is that causing the death of a parent would be contrary to the obligation of good treatment and respect towards them:
ووصينا الإنسان بوالديه حسنا
And We have enjoined upon man goodness to parents.
— Quran 29:8
One may answer this by logic in the following way:
If we accept and believe that Allah is just, then his shari'a is just so seeking an award outside of Allah's rulings must be a kind of injustice and denial of Allah's justice and shari'a which implicates that this is kufr (rejecting the truth)!
So basically there's no difference between a judge who instead ...