To be clear and answer to a comment: I don't need validation for my actions, the validation came from the aftermath. I am however asking for alternate methods and I'm narrating the story for context and what I did so people don't repeat the same method I already know and tried. Please read the bold paragraph to understand what I'm looking for as a result of the alternate methods offered in answers.
Defusing wrath without offending the person.
The other day we were at my sibling's home having a great time until someone complained about how mom makes awkward mistakes using social media.
Initially my siblings and I seemed to have the same goal, to remind mom about being careful on what she does in social media to avoid hurting sensibilities or cause misunderstandings. Mom tried to explain the steps she took as to let us know she had been careful. This lead me to understand she didn't know how to use the mobile version of the app. It was the end of the issue for me and I tried to change the conversation.
But my siblings went on and on complaining, which became about their own misunderstandings and lack of healthy communication. Mom was fast to recognize that and brought her concerns to the table on how they're not exchanging more fulfilling communication.
To be clear, weaker target doesn't necessarily mean weaker person, in this particular situation mom was in a weaker position because she is staying at their place.
My older sibling has an irascible personality and kept complaining about all the anecdotal and hypothetical ways on how the way she uses social media discomforts others, aiming to win the argument because in their mind, this will change mom's behavior. It got bad. My other sibling withdrew from the argument when we noticed our older sibling had lost their cool.
The yelling didn't stop even when our older sibling noticed and pointed out how mom's breathing became agitated and instead of taking that as a cue to go easier on her or choose a better time to talk about the issue (or recognizing their own breathing was more agitated, for that matter), instead took it as an additional thing to judge her character. Failing to see the bigger picture, went on and on complaining and highlighting the same "point" from different perspectives which by now was pointless because mom was already on half-listening mode, looking down at her phone feeling anxious, doing shy gestures and all types of non-verbal cues my sibling seemed incapable of noticing under wrathful mode. Mom was effectively taking a verbal beating, and my attempt to intervene was countered with a dismissive lash-out.
The technique I know:
I have some psychological training and I've found the reflection strategy to be very effective even if confrontational, this puts the pressure on me rather than the original target.
The reflection strategy works for similar reasons that a mirror on a room deters inappropriate behavior, but there were no mirrors around for zir to see zirself on this angry state.
The reflection strategy can come out as childish if used incorrectly, it consists in letting the person talk until something useful comes from their own mouth, and use it to highlight their wrong behavior by mimicking their own line and their own attitude.
This is not the first time I use that tactic, it usually has success ranging from mild to great, at the very least resulting in the argument going down in a decremental tone. But this time didn't work well.
My last attempt was to point out mom was already defensive and any further attempt to communicate under the same aggressive terms would fail. This fact hit a spot, but the beating went on, regardless.
The technique I had to improvise:
Detecting I had an ally on the table, the spouse who was noticeable anxious about the possibility of me and my sibling escalating the conflict, I invited the rest of individuals present at the table for a table/board game, the spouse was fast to concur and went for the cards and sat next to me and started shuffling them.
My other sibling declined to participate, but the spouse's involvement was enough to break the tone that dominated the surrounding space and the argument went on fast decline until my previously angry sibling asked for cards to be handed to them before their spouse finished shuffling, then made us wait until finishing some sentences already on their mind before lifting the handed cards from the table, but that didn't take too long, about less than 2 mins. That last gesture made it clear about their intent to dominate the space, but that is just one single element of everything that was going on. Mom refusing to play after the argument was done was her way to convey she didn't feel welcomed. We didn't keep playing but the episode was over (I can't call it fight because it was unilateral).
What made me notice this wasn't the best method was that my sibling is not an asshole but my intervention made everyone notice their asshole behavior, additionally, I was worried about Mom's feelings. So after half the table showed no interest to play and the rest couldn't decide what to play and the conversation went stale, I got up and said that I felt like taking a walk around the neighborhood to "digest the sugar" as a pretext and invited mom to tag along, she was fast to join and went to change her shoes, meanwhile, my sibling looked like feeling guilty, we all needed to switch scenario so I invited everyone to tag along, I specifically invited him/her. My intention was to convey a "let's calm down, let's leave this behind". The response was actually much more positive than I expected and we ended up outside looking at the stars and having a good time again.
While I sort of consider the night a success, and while I know they have their own relationship to fix, I would like to know an alternate method.
How can I tactfully defuse anger before it escalates to protect a target from taking verbal abuse?