When talking about emotionally-charged topics like this, my general advice is to just state the facts and let the readers make their own conclusion. You never want the readers to feel like they are being emotionally manipulated, and I find that staying factual (as much as possible) minimizes this risk without being any less powerful.
I also agree with
@gonnif that no one sees those in abusive relationships as being willing participants.
With regards to mental health, there still unfortunately remains significant stigma against it (in part due to our cognitive biases from seeing medical students crash and burn due to uncontrolled depression, etc). However, things are slowly changing and it's no longer the death knell that it used to be. I have seen some very powerful and compelling essays written on this topic that reflected very positively on applicants. Of course, for every essay that helped, there were many more that hurt, but usually due to the way it was portrayed.
If mental health is mentioned in an application, adcoms need to be reassured that it won't become uncontrolled again during medical school, residency or beyond.. usually through demonstration of sustained periods of wellness despite recurrent adversity and stress.
Depending on your own experiences and comfort level, it might make sense to discuss one or both of these experiences. However, if you do write about it, be prepared to talk about it during interviews as it will almost certainly be asked about. If you do end up deciding to mention mental health, feel free to send me a DM and I'll be happy to read over it to see if it's cringe-worthy or not. Best of luck to you.