According to Islam, children are like a property for the father, just like slaves are like a property. And a father could not be killed (or given any other lighter physical punishment, or to send to the prison) for killing his children, just as he could not be killed for murdering his slave. 

Musnad Ahmad bin Hanbal (link):

It was narrated from Umar that the Messenger of Allah said: `No father is to be killed in retaliatory punishment for his son`
Grade: Hasan (good)

لا يقتلُ بالولدِ الوالدُ
father is not killed for the son."
Grade: Sahih according to Albani (link)
Albani also gathered all these traditions from different chains here (link)

Allah Islamic Scholars are unanimous if a child kills his father or mother, then he will also be killed in Qisas. But if a father kills his children, then there is some (minor) difference of opinion about it. Imam Abu Hanifa, Imam Shafi'i and Imam Ahmed bin Hanbal say that father will not be killed in Qisas. While Imam Malik differed slightly and he says that if father had "slaughtered" his son, then in this case father could also be killed in Qisas but if father killed him with a sword, then no Qisas will be taken from him. 

 

A ‘celebrity’ Saudi preacher accused of raping, torturing and killing his five-year-old daughter has reportedly been released from custody after agreeing to pay ‘blood money’.

Fayhan al-Ghamdi had been accused of killing his daughter Lama, who suffered multiple injuries including a crushed skull, broken back, broken ribs, a broken left arm and extensive bruising and burns. Social workers say she had also been repeatedly raped and burnt.

Fayhan al-Ghamdi admitted using a cane and cables to inflict the injuries after doubting his five-year-old daughter’s virginity and taking her to a doctor, according to the campaign group Women to Drive.

Rather than getting the death penalty or receiving a long prison sentence for the crime, Fayhan al-Ghamdi served only a few months in jail before a judge ruled the prosecution could only seek ‘blood money’.