There is no software that can protect a you from another person who thinks it's amusing to find something disgusting on his device, and then tricking you into looking at it, just so he can laugh at your horrified expression. Many people are simply jerks. I wish it was possible to protect kids from the awful stuff that is out there. It's not.
I don't blame you for trying to do what you can. I just know that I never sought out violent and gross content, but I definitely saw it. When I was in elementary school, no one had access to the internet, but kids were finding ways to get their hands on "Faces of Death" on VHS. There's no software to prevent that. I wonder if you wouldn't be better off exposing your kids to violence in a controlled setting and then talking to them about what they saw than you are keeping them totally innocent, and then leaving them to deal with their initial exposure to horror on their own.
Furthermore, I know that when I was a lad, as soon as I was aware that I was being "restricted" in some way, getting past that restriction became my new mission in life. I'm sure your children are clever. They will probably defeat the software in some novel way that you didn't imagine.
What the software does get you is the ability to say "ah well, I tried". And that does have some value, I suppose.