First of all, do NOT return home under any circumstances, it will end in tears. I was in your position once and got myself a room in a house where I looked after their animals in return, rent free, those sort of options are available if you look hard enough.
Secondly, your dad has developed his own 'coping strategy' which is why they have been able to co exist. He probably would worry sick if any thing happened to your mum, despite how unreasonable her behaviour. My dad stands my my mum in the the same way (but not so extreme).
Thirdly, your mum cannot help herself so please do not take the unreasonable, irrational rants and personal insults to heart. Please view her with pity and do not rise to the bait when she goads you.
Unfounded accusations that are so absurd made by a mentally unstable person are not something you should get worked up about at all and so please do not get angry or give her any fuel to continue the gibberish.
React as you would do with a patient who has very bad health, can you give pity and compassion and be sorry for her instead?
Check your reactions next time, you can't alter her but you can alter your own reaction to her.
Please don't give your dad a hard time, he probably gets it in the neck on a daily basis.
Look after them both but don't get involved in her slanging matches, say 'oh dear' instead and perhaps write a list of all her gripes if she is unstoppable, then you can analyse at a later date with her (when sober).