This is a horrible situation and not sure at all what I'd do but I don't think I could do nothing. There's worse to come if left unchecked. Think of it that way.
One day those little kids - if they survive that long - will be teens and you'll be sure to be facing vandalism, etc. just for kicks because they've been living in those conditions for a decade.
On the cat hoarding, my great aunt I referred to lovingly as the queen of cat ladies. She had a big old place - not a dive like this, a gem - out in the country. Three stories with a wrap around porch way out in the country down a dirt road. I'm kind of nuts for cats myself and would love to go to her place for literally a cat everywhere you looked outside.
She did not let them into the house. They sheltered under the porch which was warm enough in winter between keeping wind, rain, snow out and the heat from her house. She just put a water and food bowl every couple of yards on the porch that ran all the way around the house and let them breed and breed. Upon her death, there was only one way to remove hundreds of feral cats and I'll leave it at that and spare everyone the grusome details.
I'm not in your shoes and so can't tell you what to do. I'd be afraid to act too if I were in your shoes though me being me, I don't think I could watch that day after day. I just warn that it will get worse when those kids become teens. And you may be none too safe then either.
I'm in upstate New York and one place growing up between the country and suburbs, we had two such families and when those kids reached their teens, they became hellions. There was also one place well kept but the two teen boys were terrors and ran unchecked. One grew up to be a literal axe murderer. (You can google his name and find the story but I'm not giving it because too close to doxxing myself.)
Problems ignored tend to grow worse. Not go away. But my empathy because what a hard place you are in.