Hi @Daisy
I’m sorry to read what you have experienced.
Yes, you can apply for the permit under §31 Abs. 2 AufenthG. That part of the law is specifically for cases where the marriage has been for less than three years. For people who have been in a married relationship for over three years, the first section of paragraph 31 applies.
Section two creates an option for hardship cases (in German ‘Härtefall’). The text states that such a hardship is particularly clear in the case of domestic violence. It does not, however, specify what documents must be supplied to prove this. Based on what you have written, you can submit your own statement as part of the application, medical reports relating to the domestic violence and its consequences, the police complaints and house bans.
It is good you have a lawyer and are seeking further legal advice. I presume you have a lawyer for family law and are looking for legal aid for criminal law. You can also apply for legal aid to speak with an immigration lawyer on how best to prepare an application for a residence permit according to paragraph 31, section 2.
If you feel you need additional support aside from legal advice, it may be worthwhile contacting the organisation ‘Weißer Ring’. They assist individuals who have experienced domestic violence. Among other things, in some cases they can provide some financial support. Here you can read more about them:
https://weisser--ring-de.translate.goog/haeuslichegewalt?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en&_x_tr_pto=wapp
If the commission-based job is not enough to support yourself, you can apply for the social welfare benefits Bürgergeld from the Jobcenter or Wohngeld from the Sozialamt. Getting these benefits does not affect you getting a resident permit independent of your husband.
Best,
Éanna