As long as people can get away with grieving, they will continue to do so. If the only penalty is having to say "I'm sorry", then the grieving won't stop.
The same goes for threatening people with a ban. If you don't execute your threat, the threat of a ban is meaningless.
Take my advice: be strickt but fair.
People will hate you for banning them. But people will also respect you if you use the banhammer fairly. Right now it's just a mess and nothing is gong to change because you rant about it on the forum. What kind of mod do you want to be? One that is friends with everybody? Or one that keeps the server a nice place for the majority of the people?
You have the tools to keep people in check. You can ban people for a day, a week, or permanently. But don't threaten people, just ban them already.
Also important, let people know you've banned someone. Make a thread on the forum why someone got banned, and how long the ban will last. Then lock the thread, there will be no discussion about bans. If people start whining about their ban, then ban them from the forum as well. That way people can see that there's no messing around with the rules and the mods enforcing them.