This might sound horrible, but have you or your parent(s) ever considered a care home or something? It's obvious that having her around is not doing you or your mum any favours and it's probably having a very big toll on your mum as well, maybe even moreso than it is on you. Whilst your little sister isn't to blame at all, because she literally doesn't know any different, it doesn't mean you should accept it at the same time.
I would perhaps ask your mum if she would be willing to maybe see if she can get some 24/7 care in a residential place or whatever the next time she loses it with someone or something and ruins your house even more. You shouldn't have to suffer because of her, even if it's not her fault as a result of a mental condition. They'd also provide better support than you or your mum are capable of given they'd have 24/7 supervision too, plus they'd have a strict routine which would help your sister settle in more given she's autistic. It seems as though that'd be the best move, although I have a feeling that if your mum is putting up with it, she might not want to get your sister the help she needs because she feels solely responsible for her and putting her in a home would be nothing short of disrespectful. That's how most of these situations end up getting to this point.
