I've had similar issues with a different kind of condition, both with parents and with a neighbour whose answer was to shout and rave if something wasn't as they wanted.
What I've found in both cases, was that the wording I used to explain it, was critical, and they won't want to move, but will in fact move. Probably quite quickly.
There is a twist in your case, to deal with first. If your mother is using this as a way to vent frustration by stressing you - a kind of "power dynamic" update on kicking the dog when you feel annoyed - and she's mentally going "I'm stressed, I could give a shit, you can have some stress as well" when it happens, then you also need to deal with that by ensuring she figures its not in her best interest. If she's just volatile and stressy, then you will need her to learn self-control instead.
In either case be aware that there is a chance that solving it will mean going face to face with her bad behaviours, but on your terms. After all, if what she was doing wasn't (for her) a great approach psychologically speaking, she wouldn't be doing it. Reasoned explanation isn't helping. So you need to undermine and remove that, and make calm resolution on her part more advantageous, not by reason, but by changing the way it plays out - changing how you respond. She won't like it, obviously. Perhaps nor will you. People like the familiar.
Let's get to actual tactics.
Situation #1: Ranty neighbour
The neighbour situation for me, came to a head when she was ranting about something, ignoring everything, not letting me explain, with 2 family members attacking as well any time I tried.
I fell back on the most crude of measures: "Jane [not her real name] be quiet and listen Jane be quiet and listen Jane be quiet and listen Jane be quiet and listen Jane be quiet and listen Jane be quiet and listen Jane be quiet and listen Jane, be quiet and listen Jane be quiet and listen Jane be quiet and listen Jane be quiet and listen Jane be quiet and listen Jane be quiet and listen Jane be quiet and listen Jane be quiet and listen Jane be quiet and listen Jane be quiet and listen Jane be quiet and listen Jane be quiet and listen Jane be quiet and listen...." Over and over and over, quietly and constantly, in a dull bored as hell monotone without pauses, until the message got through.
Eventually she shut up and did. Then I said simply, _"If you shout, I can't help you. If you don't listen I can't help you." Then I waited, and when she stayed quiet, explained. Just once. If she had ranted again, I'd have repeated exactly the same, and repeated, and repeated, until she paused, waited and had a civil dialogue.
And oddly, she's never tried that since, even once. In fact she's become very civil to me.
Situation #2: Reactive shouty parent
The parent one, they wanted to help but were stressed. So I could be more engaging. I explained (as you did) that when they shout, it's really hard to stay calm and not react badly (which was the issue we had between us with shouting). But it didn't work, because so often emotion trumps reason. So I tried two things.
First, I picked a calm time when they wanted to be interacting nicely, and told them in simple terms, that I couldn't do what they wanted if they shouted. I used words like I need...,and I just can't..., rather than pitching it as a preference or social niceness. I used words like When you [this] my brain goes [that] rather than 'I have XYZ mental health condition'. I explained the immediate cause of my reacting: and its really painful even if that doesn't make sense to you.
Second I didn't argue (they'd just shout more). I simply found a reaction that they un-liked enough that shouting became unliked too, and listening became better for them. Same as with the neighbour. In their case, the moment they shouted (ignored what I'd said about what I needed), I just walked to my room and shut the door, and refused to talk or engage other than "Get out. Get out. Get out. Get out. (etc)" if they came in. Essentially looking for a passive-aggressive countermove/reaction that takes me out of the battle and disfavours shouting over listening as a tactic.
You can mentally imagine the unspoken counter-statement as saying, "If you're going to do that, I'm not going to help you, and you can rant with no reaction (at a door) if you have to rant at anything."
Basically I decided to deny them a verbal confront when they did, and let them have the last word if they insisted. A very hollow unhelpful victory.
Eventually they did listen. And using the words above, I explained. I had to do it more than once. I occasionally had to do heavy duty aggressive parental guilt tripping too ("You don't care about me do you. All I've asked is to tell me quietly, and you can't even do that. Just go away"), and refused to engage till they have finished taking that on board. Eventually, it worked.
Wrapping up and summarising
So those would be my tactics.
People find change hard. What they are doing suits them given what you're doing, even if useless. They feel ok or vindicated or right about it. Explanation doesn't work. So you need to change the dynamic, or change what they do, by making it deprive them of the reaction that sustains what they're doing and makes it pointless. Unfortunately its games against games. So when you see them drop theirs, you need to drop yours too, to give peace a chance. You might need to do that many times, but eventually it'll work.