I’m not going to comment directly on the video. Rather, I think it is worthwhile to give my answer to the question asked. What does a woman who is abused do? (Note also that I’m aware there are men who are abused, but the question was not framed in that way.)
My answer is simple: Get out of there and report it. But especially get out of there. Don’t give a physical abuser the opportunity to do more damage.
I am an egalitarian as I have stated on this blog any number of times, yet I won’t criticize complementarian philosophy as natural leading to abuse, as some have done. I treat this issue as a non-essential. Complementarianism is not abuse.
Violent abuse, on the other hand, is a crime and not just something to be dealt with in connection with the church. It remains a crime irrespective of the theological positions of the abuser. I think we’ve had enough cases of church cover-ups. I also cannot see any way in which abusing one’s spouse or one’s children can be justified, or that one ought to endure it. It should be reported.
Many women in such a situation would not feel comfortable taking their case before the church, especially with a husband who might be in a position of authority, or where the church leadership is all male. In such cases again, I would always emphasize getting out of reach of the abuser first, then reporting it either to the authorities or to someone trustworthy who will, in turn, report it to the authorities.
For me the key theological issue here is that abuse violates the divine mandate for marriage. For some it seems to be easy to hear “wives submit to your husbands” (Eph. 5:22) without also hearing “be subject one to another” (Eph. 5:21) and “love your wives as Christ loved the church” (Eph. 5:25). How was that again? “As Christ loved the church and gave himself up for her.”
That’s the New Testament idea of having authority.