It’s even worse than that, in the US police have broad latitude to destroy property, kill pets, seize any cash or assets (theoretically related to the crime, but very easy to abuse) and etc. while executing a search, with little to no recourse.

Not just kill pets, but kill people. Even if they raided the wrong home.

Yeah, it’s true.

I think it's fair to expect that the authorities must have a very good probable cause to perform a search of your home, and that any search that turned out to be unwarranted results in a big compensation and a public announcement stating that the specific police department and judge violated the right to privacy.

I'm guessing search should still happen in a way to limit damage (physical, psychological) to other parties (in this case, the kids present).

You could sue if they made some major mistakes or were fabricating evidence or some other significant malpractice. It's a pretty high bar.

You can but chances are you'll still lose.