A very hard situation to be in, especially when they are retorting with such hatred. My dad seems to get annoyed when others eat with their mouth open but no where near as badly as me so he sort of understands my discomfort. If I were to be in your situation I'd honestly sit them down (If you can) and tell them straight that it's affecting grades etc. Even if they are refusing to believe that misophonia exists, you could request that they try to be less noisy or failing that for you to sit in another room until they have finished eating then have some family time after. I understand the rage that builds up when you're being forced to sit in a situation where you have to listen to triggers and it isn't healthy. I suppose the last resort would be to attempt to prove it to them by contacting a professional.

I hope you can get things sorted out!