Healthy women in healthy marriages don’t avoid the mikvah as punishment. Perhaps if the husband is unwilling to discuss the problem, I could see a woman using that as a tool (not that I agree with that – I think if for nothing else, a woman should go to the mikvah to remove harchakot). What you are talking about is either not a healthy woman or not a healthy marriage. And its a power play, not a good sign for the marriage either.
The reason abuse usually refers to him abusing her is because something like 90% of abused people are women.
No man should stay in an abusive relationship either.