I would rather be alone than be with a partner i do not trust.

This person has severe mental health issues. You didn't cause them. It is not your job to fix them. Your priority is the safety of your son, her girl and yourself.

Threatening to harm herself is a way to keep you trapped in her illness. Along with all the other behaviours.

Call child services and file a complaint . If this is not possible, call 911. (112 in France)

What you have is far too volatile and dysfunctional to be considered a relationship, so ease up with "it's her or nobody" argument. Maybe she is the one for you, but until she gets treatment and is healthy to be around, you must stay away.

Where is the girl's father in all this?