If the Sith in Amorosa's family aren't part of the Baanite Sith, what keeps them from turning on each other? Bane established the Rule of Two specifically to keep the Sith strong and keep them from weakening themselves through betrayal.
Most discussions about the Sith start from the premise of "Bane is an idiot."
The Rule of Two is actually really fucking stupid when you think about it, because even a single slip up means the end of the Sith entirely. It also requires the Master to accept their demise as an inevitability, which is about as "un-Sith" as they come.
Which makes sense given Bane got most of his ideas about power, strength, the Force and the Sith from a fucking Jedi. This is just something that happens when Jedi become Sith, they turn into these weird, grunting ogres obsessed with machismo.
As for the Beniko Sith, what keeps them from turning on each other is extremely simple.
Betrayal is not an inherent aspect of the Sith. Many Sith simply view being in a position of power to having power in and of itself, so they're inclined to take the shortest path to success. This is actually one of the biggest failings of the Baanite Sith: Eventually you have to stop skulking in the shadows and actually do something, and that's the part where Bane's Sith always fuck up.
The Sith are defined by the relationship between Strength and Power, and their own relationship to it.
Baanite and Revanite Sith are fascists, so they seek symbols of power to demonstrate their own. A core tenet of fascism is making weak men feel strong by enacting violence against others for them. They claw and scrape for power and authority because these things signal to others "I am strong, do not fuck with me" which only invites other insecure, weak men to want to stroke their own egos by fucking with them.
This philosophy is heavily colored by the large number of Baanite and Revanite Sith who are fallen Jedi, bringing Jedi perceptions of the Sith and the Dark Side with them.
Beniko Sith philosophy is about fundamentally bettering yourself. It's about being strong instead of looking strong. It's about being an actual leader, protecting your people with unrelenting ferocity. And if you're not the one leading, then you clearly haven't bettered yourself enough. Work harder.
The Revanite Sith are all in on slavery because it makes them feel like a big man in charge of all the serfs. The Beniko Sith view this as pathetic for this exact reason because if your authority has to be maintained through force, then you never deserved it in the first place.
For Beniko Sith, displays of power are very different: No poverty, everyone is fed and happy, security is not even a question, nobody has to be forced to contribute or to stay because they are happy to do both of those things. Loyalty is worth more than fear would ever be.
To translate this to the real world: For all the United States' military bravado and trade coercion, we've always known that nation was as weak as they come because they have all that wealth, and still their people live in extreme poverty. A real leader would consider that the highest embarrassment possible.
What keeps the Beniko Sith from turning on each other is that any Sith that is so pathetically weak and insecure as to want to betray their Master in the first place... couldn't.
Say you're Darth Estrela and you decide "I'm going to betray the Dark Lady and take her place!" Amorosa's going to turn that into a lesson in humility because you aren't a threat, you're a student who has briefly lost her way.
