Hello Luna23. Welcome!

That's very rough. Sorry this is happening.
My mom was diagnosed with BPD a few years ago but she's had it all my life. She refuses to get treatment. I'm her daughter.
She's verbally, emotionally and physically abusive. If it weren't for my dad stopping her from learning to drive and get a job outside the home, she would be on the same trajectory as your mother. She has no filter to her actions.
I don't know where you are writing from and laws on this vary. In the US, where I live, you can have someone declared legally incompetent if they are unable to manage their own affairs through mental illness or disability. You could force her to be committed to a psychiatric hospital for inpatient care if she has this designation. The government may take care of all or part of the costs.
I don't know how high or low the bar is set for that. I never went that route with my mother. I know a few posters here have.
At this stage, you cannot force your mother to do anything. I know it's upsetting. I have a very limited relationship with mine due to her abuse taking a steep toll on my mental health.
I try to remain calm and collected the one time per week I see her. I don't feed any drama or trouble she tries to create by goading me. I nod slowly and acknowledge that this is too bad or I'm sorry. It's called gray rocking, a communication tool to use with difficult people.
My mother dysregulates to discharge the immense stress and lack of self people with BPD generally have. It never goes away no matter what I do. I try to protect myself to make sure I don't fall into the Karpman Triangle which is a not too healthy communication style based on the imbalance a mentally ill family member causes to the family system. There are lots of other resources on this site to help you cope and decide upon what is right for you --articles and suggested books.
Therapy has helped me with many aspects of my mother's issues. I meditate which helps calm me down quite a bit too.
Am not sure about your other family members such as father or other siblings besides your brother. Are there others in your immediate family who acknowledge there are issues with your mother? That can help a lot.