Suit yourself, Zec. Meanwhile, here's what this looks like in practice:
If there is evidence that a man associated with Biblical Families is beating his wife, then that man can expect a call or a visit from someone associated with the leadership here. We will with all the love in our hearts encourage that man to step up to his high calling and the scriptural instructions regarding how he's supposed to treat his wife (start with the "weaker vessel" passage and work outwards from there), and pray for his progress in being a better man. Should that process fail to produce positive results, or worse, should that man belligerently defend his right to continue to beat his wife with impunity, that man will find himself not welcome at Biblical Families. If we believe that the woman is so beat down emotionally that her safety is at risk and she is unable to defend herself or seek refuge (or if children are also subject to domestic violence), then intervention by law enforcement may be appropriate.
[Side note: I have to clarify because of the interesting times we live in that I am speaking of "domestic violence", a term you used that has a specific legal meaning. I am not speaking of consensual "domestic discipline". However eyebrow-raising that idea may be for some, what consenting adults do on their own time is not the subject of this post.]
I do not agree that because the Mosaic law does not include a remedy for what we would call domestic violence, the elders of churches and leaders of parachurch ministries are precluded from enforcing standards that they believe are appropriate for the organizations they shepherd. The descriptions and examples of the ministries of the leaders of the NT churches suggest otherwise.
We may need to go back and tie up a few loose ends. This part of the discussion started with your claim that a husband's actions toward his wife are not subject to the judgment or interference of others. But later you mention intervention and taking a wife away from her husband, as well as divorce, or a "cessation" (presumably also a divorce, or cessation of the marriage), so I'm not sure what all kinds of "interference" you had in mind originally. My first comments were directed at the idea that a man would think his actions are "not up for anyone else's judgment".
Manly men relate to each other as a meritocracy, as honorable men seeking the company of other honorable men. A man's actions are always subject to review and judgment by others—by all those around him, but particularly by the 'honor group' of other men that he primarily associates himself with. This particular group known as Biblical Families is here to promote healthy, vibrant, biblical marriages and family structures. We're not going to take any man's wife away from him, and we're not going to endorse divorce as the solution to marriage difficulties. But on the spectrum from judgment to interference to intervention to breaking up a marriage, you can expect that others others here will judge your reputation as a husband, and possibly even 'interfere', if that's what you call unasked-for advice about how you can be a better husband.
Final thought: The "Christian polygamy movement" is lousy with chest-thumping, knuckle-dragging "patriarchs" with a low view of women—all it takes is a couple of hours on facebook to figure that out. Those guys are mostly theorists, though, or guys with bad track records or with obviously miserable or belligerent wives. The families I know that are successful, though, put the emphasis on love. We as husbands put the emphasis on loving our wives, and we as brothers help each other to love our wives better. That's what we're about here, and it is important for any family considering this lifestyle to get that right from the get-go.