I'm so sorry to read that you are feeling like this @Randomword6 
There seems to be an awful lot going on to stress you. You are estranged from your partner but still living under the same roof, yes? That in itself is not a good situation to be in - is there any prospect of you getting separate places? Five adults under one roof has the potential for so much noise and chaos.
Are there any solutions that would work for getting a better night's sleep? I hesitate to say earplugs as they bring on tinnitus for me, but they work for some people.
Re. your outburst after losing your mother (I'm sorry for your loss) - if ever there was a time when you deserve forgiveness, that would be it. You should try to forgive yourself.
You say My daughters have both acknowledged that I am routinely contradicted, dismissed and disagreed with on almost everything - have you talked to them about how that could be resolved? Again, five adults under one roof are bound to disagree. As adults they are old enough to understand the need for compromise.
Re. throwing and breaking things - you need a strategy in place to do something when you feel like this - I would suggest leaving the house straight away and walking until you feel calmer. It is understandable that your family are troubled to see you do this. Can you talk to them about what you will do to reassure them that you will find a way to manage things in the future?
It's really good to read that your family, despite everything, are your reason to live. You need to build on this feeling.
What is your family's understanding of your autism? Are any of them ND themselves? Talking about your condition and what is triggering for you - perhaps encourage them to research it online - might make them feel a little better about the stressful situations that are arising.
I'm sorry I don't have any more robust suggestions. I'm not a parent, hopefully someone who is a parent of teen/adult DC might come along with more constructive advice.
I do hope you can find a way through this soon, to a better state of mind.