I don't think it's anyone's place to decide there's one better way to deal with tragedy.
It depends so much on the individual, the circumstances etc.
I tend to be ok as things are happening, and very much need to carry on with work etc, and then I do need time afterwards. But I need that time whatever happens before, and it's irritating the way some people seem to think it was 'catching up with me' with the criticism that if I'd have behaved as they wanted at the beginning is somehow be able to skip the grieving process. It's a well worn meme, the idea of someone carrying on and then falling apart and the 'carrying on' being the person (the actor really) refusing to face it, or somehow being in denial. It's a very annoying meme!
As I've lost 2 of my close family now, in different but equally horrific ways, I do sadly know how tragedy and grief strike me.
Where as so many other people only have TV and film stories plus some tabloid hysteria thrown in. Which is probably going to make things harder for them as their own grief process might come in a different way from the Hollywood narrative devices.
There's a lot of self interest in others when they try and push their own assumptions into someone else's life. It's about them wanting to minimize, sanitize and control death. And their own fear and weakness motivates them to behave in disgusting and vile ways. Grrr. Low tolerance for this.
Another colleague had a different but still perfectly reasonable reaction to the death of her loved one where she really struggled as it was happening, and found it really hard to get through (though still wanted to work but less and flexibly), but afterwards, she found it much easier to cope, when the anticipation and the watching and waiting limbo had ended, and she came back to work 2 days after very composed and threw herself into work. Which is what she needed to do.
Doesn't make her strong, or callous, or in denial. Just like my experiences didn't make me stupid, or weak or in denial!
Both are fine. That's just the way it happened for us. And there will be your way and that might change or develop differently as it all happens too...
Your colleagues foul gossiping and bitching is the last thing you need right now. What is management like? Can you pass this on to them, saying that you don't want to have to deal with it, and won't be mentioning it again, however these people need to be told that their behavior is both unprofessional and vile, and their behavior and voices need closing down.
Would you be able to do that? Depends on the company I know, mine would be on it well if I could go via a manager, though if I had to go through HR directly it would make it worse as the person I'd have to deal with would glory in the drama herself.