@Petnavis What you are implying is that nobody should help anyone, because anyone could be a criminal, and that the potential of helping a criminal is morally wrong.
I use the word child to describe a parent-child relationship, because everyone is a child of a parent, regardless of the age. A child in this sense is simply a direct descendant of a parent. A 50 year old is still the child of an 80 year old parent.
The characters are under 18 years old so they are not legal adults. At least the MC, but I'm not sure about the others. But age doesn't change responsibility, although it may change the allowable punishment by law.
No, parents cannot be held for crimes committed by their children by law, even if the children are under-aged, at least in western democratic countries. Otherwise it would be like making a child responsible for the parent's debt when the parent passes away, which is not true in western countries, although Japanese manga seem to make it so.
It is entirely possible that parents never taught their children to commit crimes, and the children learned to do it on their own or were influenced by other unrelated people. Automatically making parents responsible without any evidence is against the law in most developed countries. People are innocent until proven guilty. The story so far hasn't shown that the parents were involved with their children's crimes, although it does imply that they tried to shield their children from attention by sending them overseas, which isn't a crime. The story so far may show that they could have abused their powers in their jobs, but so far not in relation with their children, at least until the MC started to kill them. Let's say for example, a restaurant owner sees hungry people and feeds them food for free, but the people he fed turns out to be criminals on the run who later commit more crimes. Is the restaurant owner guilty of assisting the criminals of their crime?
If you want to find real world similarities to the story regarding revenge, you can find several in the news from middle-east/asian countries where revenge acts or revenge killings are allowed by some tribal or religious cultures. Like if a parent or child commits rape, the victim's family is allowed to rape a family member of the criminal. It's completely against the law in western countries. Or if someone causes an accident that causes a victim to lose his eyes, the victim's family is allowed to surgically remove the eyes of the person who caused the accident. The US constitution's 8th amendment prohibits cruel and unusual punishment, and I assume most developed countries have similar laws, although this would apply to the person who commits the criminal act. Punishment to family members who have not been proven to be involved in a crime is something different.