How does a psychologically normal human react to having their innocent child splattered? I will be ignoring the parts where common sense is correct.
First, the denial. They will appear to double down on clinging to the ingroup. It's a reflex: in times of trouble, don't rock the boat. Appear particularly loyal. Similarly, beliefs have some inertia. They do not change immediately even against overwhelming force.
However, it will quickly be clear that the ingroup is offering no substantial support. Words and theatre is all they have. This will feed the previously-repressed feelings of betrayal.
Now it's time for the anger and spite. They will defect on the ingroup and join the rebellion. They will join the KKK or the unironic Nazis, as the only groups that seem harmonious with the hate they now feel. It will be years before they realize this isn't working, so I'll stop the story there.
If humans genuinely cared about other people's children like their own, there would have been a semi-spontaneous mass violent uprising after the first terrorist act that really counted.
Some don't count. The very first one gets written off as a fluke. Weird things happen sometimes, it's best to forget about them. There are more weird one-off events than normal events, a normal human can't spend time thinking about them or that's all they would do. The second one triggers the denial phase. They realize it's a pattern but they hope someone else will deal with it. But the third or fourth one would have brought down the government.
At the very least there would have been mass civil disobedience, after everyone simultaneously became a Nazi under a noticeably non-Nazi government.
"Hey neighbour, you paying your taxes this year?"
"Ha! Not if I can avoid it."
"No? Perhaps I won't either."
The IRS cannot deal with 70% of the country paying their taxes. It would be an undeniable vote of no confidence in the government as a whole.
First problem: modern humans are not psychologically normal. Prussian school is designed precisely to lay waste to all facets of normal psychology. (Homeschoolers are darkly funny. "If I implement Prussian school at home, it will be different, right? Poison administered by the ingroup is different than poison administered by the outgroup, you see.)
Second problem: nobody gives a shit about other people's children. Well...they're small and easy to kill, plus killing the outgroup's kids makes more room for the ingroup, so it doesn't besmirch your cooperator credentials. And killing is fun. But beyond that nobody gives a shit about other people's children.
Final problem: modern populations have been bred for millennia to be extraordinarily cowardly in the face of state decrees about what is and isn't high status. The Romans managed to outnumber the brave races who would have resisted, and subjected them to Roman Peace. The brave minorities in broadly cowardly races were systematically weeded out. They will join the Nazis in their heart. But they won't dare to so much as tell anyone.
There are some other indicators. If your child dies, you worry about the mental health of their siblings. If it's your grandchild, you check on the parents from time to time as well. Where are the repeated newspaper articles about how the children are recovering, or not? Where's the frankly troublesome avalanche of letters asking about it? Why don't the survivors have hundred or thousands of offers to take them on a trip into town to help take their mind off things? Where's their legions of volunteer bodyguards?
It's taken for granted that nobody gives a shit about other people's children...except when it's time for us all to pretend to care, in service of whatever selfish impulse can be served.
Of course the government is fully aware of all this. Being well-socialized, they know that, like themselves, nobody cares about other people's children. The rulers know everyone is amazingly cowardly, just like they are. The rulers know there's not going to be a mass wave of tax revolt just because the government isn't doing what everyone pretends their job is. The rulers are pretending too. They know.