You keep threatening to take her to court about Lexy, but you don't do it. So of course she doesn't believe you. It's just a silly manipulative threat on your part.
And you are worried that if you do, you won't see Lexy. But a judge will decide that, not her, if you take her to court. And yes, maybe the judge will decide you don't see Lexy. Courts do not put the best interests of children first. They put parental rights first and family reunification first. But taking this to the courts and to CPS will have one benefit even if you don't see Lexy again: Lexy's situation will be monitored. It will be documented. Probably eventually she'll end up with you, but it's always a struggle to get kids away from addicted crazy parents unless the parents give them up voluntarily.
You think psychiatric confinement is the answer to your daughter's problem. But that's not likely. Even if you can get her committed for 28 days or 90 days, she has so many problems they are going to take years to resolve. Bipolar plus addiction plus personality disorders plus life skill deficits plus anger management problems. And it's only fixable IF your daughter wants it fixed--which she doesn't. Psychiatric hospitals don't have secret magic wands that they tap you on the forehead 3 times and fix you (my mother also thinks that 'treatment' works this way too). There's really no point in her going to a psych hospital until she wants to check herself in. They are terribly expensive even with insurance, and usually don't work. Your daughter is not fixable until she wants to be fixed. Right now she thinks the world has to be fixed not her. I wish her luck on that.
All this abuse stuff is just ridiculous. She hurts herself and claims her boyfriend stabbed her. He's a fool if he has anything to do with her after that. He's going to end up in jail for something he didn't do. But of course, he gives her black eyes. And she provokes him and attacks him and he attacks her, and frankly, they deserve each other. They both deserve to be in jail. Thank god they are venting their insanity and violence on each other rather than the innocent people. And as indignant as you are about him giving her black eyes, his mother has the same right to be indignant about your daughter attacking her son. Neither of them is better than the other.
The only one in the family who is innocent is Lexy. Eventually their violence is not just going to be psychological and emotional towards her. Eventually they are going to hurt her directly. This is such an ugly, ugly situation. Kids with addicted parents really do get scr*wed.
I can't tell you what to do, only what I'd do, but I had a son knock me down too, and I went completely no contact with him even though he was homeless (he figured out someone else to mooch off of). I don't have a grandchild being held hostage, but with an addicted mentally ill parent, nothing gets better until either the parent decides to heal themselves or until outside authority steps in and takes charge of the situation.
In your shoes (and I'm not and can't tell you what YOU should do, only what I'd do), I'd stop threatening my daughter with court action and just quietly do it. I'd talk to a lawyer, file a petition asking for custody or evaluation or whatever the atty tells you you should ask for to make a permanent change in Lexy's circumstances, and also ask in the meantime while the case is being determined that you have formal visitation based on the pattern of visits you currently have with Lexy (every weekend?). This will prevent your daughter from cutting off all contact with Lexy. You have to talk to a lawyer.
But I'd certainly stop fighting with my daughter and certainly stop threatening her. "I'm going to take you to court" is just asking for a terrible reaction from her. You are not obligated to tell her before you do it. Disengage from her mutually violent relationship with her boyfriend; you will never be able to fix that. That's how they both choose to live, and they re-chose it every day. Sick, but god gives them free will too I guess.
In your shoes I'd focus my money and efforts on my granddaughter. First on legal fees to get her out of there if you can, and then on counseling for her to repair the damage of living with craziness and violence for the first 5 years of her life has done to her.
Where is Lexy's father? I assume he's out of the picture and in a situation no better than your daughter's situation?
I'm so sorry for your troubles. I've heard it said, it's hell to have a boy or girlfriend with addiction. It's double hell to have a spouse with addiction. It's hell beyond hell to have children with and be financially dependent upon an addict. But all that is a Day at Disney compared with witnessing an innocent child you love trapped by someone else's addiction and you having absolutely no power or authority to do anything to fix it. So you have my deepest empathy.