It didn't happen though. You didn't see it because it didn't happen. Multiple people have told you this. You have the entire internet at your fingertips to confirm that it didn't happen. You are either making it up for the sake of having an argument, or misremembering it.
People have suggested that you are - quite reasonably - confusing what you think happened with an episode of the show where Jack pretended to kill the family dog, before revealing that it was a hoax.
If this hoax is what has stuck with you for years - I don't know what to tell you. It was obviously not real in the first instance, and part way through the episode they literally yell "CUT", walk the entire family (including the 'dead' dog) into the shot and reveal that the the whole episode was scripted as part of a running joke.
To answer your question - yes, I watched the show The Osbournes (not 'At Home with The Osbournes' as you previously misremembered) when it first aired on MTV in 2002 (not on Channel 4 in the late 90s as you also previously misremembered). I also have the original box sets of the first couple of series, which were all that were released on physical media.
Disregarding all of the above, as I have already explained, neither MTV, Channel 4 or anyone else would have been able to air footage of someone breaking a real dog's neck on a light entertainment show in the UK. It simply would not have been allowed to be broadcast as you claim, due to strict guidelines around presenting footage of animal cruelty.
And disregarding that, just use a bit of common sense. You claim that the act was caught on camera, that the camera then abruptly shifted away, and the entire incident was subsequently covered up... apparently so well that only you can remember it.
The show was not aired live. It was scripted and storyboarded, hundreds of hours were shot over a period of months and edited together into individual episodes. Each episode went through multiple layers of edits and cuts by directors, producers, censors, studio execs, network execs, lawyers and the family themselves. Every single shot specifically selected and approved by multiple people. Aired to test audiences. Sent to thousands of journalists for review.
If someone had broken a dog's neck as you claim, the footage would never have made even the first rough cut. Even if it had somehow been left in the rough cut by accident, it would have been removed the second the next person saw it. Or the next. Or the next.
If someone had genuinely broken a dog's neck as you claim and wanted to cover it up, they'd hardly have scripted, shot, produced and aired another episode where they pretend to kill the family dog as a joke.
What you're suggesting is that literally hundreds of people (including the family themselves) saw and approved footage of the dog's neck being broken for broadcast, multiple networks broadcasted it illegally, repeatedly, every day, for years, sold it to other networks all around the world, then at some point decided that they didn't want any to see it anymore orchestrated a cover-up so thorough that there isn't a single mention of it anywhere on the internet.
Surely you don't believe that? And if you do...as I say, post a clip/link/screenshot... literally any evidence whatsoever of it happening, and I will apologize and make a sizable donation to an animal charity on your behalf.
Also, nobody is bullying you on this thread, don't be a silly goose.