For once, I'm going to encourage you to be an *******s, Discussion. Because your mom's being completely unreasonable here. My sister used to be a vegan (haha, she's more hardcore than you!), and the smell of meat would cause her a ton of crap. Also, I don't ever see why I should have to do someone else's dishes anyways.
Or, you know, if you wanted a compromise... tell her you'll do all the dishes that don't have meat on them if she keeps them separated, but otherwise she can just kill herself.

Odds are they're all mixed up by now, but, you know, she really should have actually put a bit of consideration towards you on this.
... Though, you know, you are a huge dick for throwing away your brother's insulin, and I honestly could not care less whatever half-assed defense you have for doing that. :/
You do realize that developing diabetes prior to the 20th century meant that you probably had at best a few years to live in constant torture, right? :O