Follow through on your plan to leave. Not only does he not care about your well-being, he is neglecting his daughter’s need for mental health treatment. 

You may never get him to accept the issues with his daughter, all you can do is protect yourself. 

Get out now.  This is not your problem to deal with.  If she is a true sociopath, the parents won't be able to admit this to themselves for years, if at all.  Sociopaths have the ability to fool a lot of people, even professionals, and they can cause a tremendous amount of damage.

Unfortunately, things have gotten so bad in our society with child-worship and with so many excuses being made for teenagers' near-sociopathic behavior on the basis of them "just being teenagers," that it is almost getting that bad now where you can't tell the difference between what some claim is "normal" for a teenager vs. a true sociopathic one.  Either way, neither you nor anyone else in your family should have to put up with this--not even for one minute!

You need to get out of there, if she’s talking about killing you (do you have evidence of this? If you do you really should be taking it to the police & filing a restraining order against the little psycho), you need to protect yourself above everything else.

If you can’t leave just yet, make sure you’re never in the house while she’s there. This isn’t just ‘kids being kids’, death threats aren’t common, nor are they acceptable or ‘just a phase’. 

Take care of yourself. Who cares if your H gets upset, he’s not the one having to sleep with one eye open. That’s fine she’s seeing a psychiatrist but that doesn’t protect you from physical harm in the meantime. Please be safe, and if you can take legal action against this girl you absolutely should.

This is horrible and so tough. I want to join in and say leave, get out of there, but I know most of us really want to find a way through whatever SK/weak parenting hell we have found ourselves in, whilst keeping our self respect and sanity in the process.

So if that's possible... first, the death threats. These are massively serious, and I know going to the police etc seems like lighting a firework, and you of course want to believe the death threats are just the rantings of a lunatic, but what do you really feel about these threats? Put aside any desire to not make them "too serious", what's your gut feeling about these threats? Do you have anything in you which thinks she may actually harm you? If so, because now you have told DH you are done, now is the time to tell him if you believe your life is at risk, and what you will do about it. If this was me and I felt it was beyond just words, I'd probably make an appointment at my local police station and ask to discuss the matter. I'd tell my partner I was doing this and say he can come if he wants.

Second, make it a rule to only talk to her when she behaves like a decent human. Video recording for evidence and all that - do not feed this, don't speak, or just say "stop bullying me" again and again for the video. Or video her back. 

I have been, and am going through, similar issues with two of the SKs, although the "Die, Die!" exclamation was a perverse wish-disguised-as-humour thing which thankfully has now gone. I know this particular SS is deterioriating, I know his behaviour is not normal, I know he's awful to be around most of the time, I know he is deceitful and a master liar with no conscience. That's one of the most troubling parts, there's just no guilt or conscience, there is no sense at all that doing something wrong is, well wrong, and shouldn't be done again. He just thinks he had to do it to get what he wanted, so what else was he supposed to do? There seems to be shades of that in your case OP.

The way I am handling the (non-life-threatening) situation has been a combination of things. I am on the verge of throwing the towel in I hasten to add, so I am not saying this wonderfully successful, but it stops me having a breakdown and leaves the way open for my partner to see the mess in front of him for himself, rather than me point it out to him, with all the resentment and refusal to see it that that route entails. So, I disengaged. If the brat says one single word to me that is rude, undermining or a lie, I either terminate the conversation or call him out on it immediately, very calmly and in just minimal words. If he argues, I leave. Unable to have a debate about his lying, and unable to play his twisted little games, he flounders and gets flustered - which I just let OH watch. I have stopped helping him with his school work. I have stopped highlighting his lies about studying and revision, his lies about his grades, his lies about the wonderful essays he's miraculously produced which I know match word for word essays he downloaded from the internet - my OH just resents me for bringing such troublesome things out in the open when he could otherwise have just blamed ignorance for them. In other words, I've stopped trying to help my OH and the spoilt brat. Sure enough, when the last set of results came out dear BM and OH got a massive shock at his terrible results. Predictable from day 1 of course. Now the serious exams are weeks away. I know he hasn't revised, I've seen him sit with the same page on the screen for an hour whilst he plays games on his phones and Snapchats with the phone slipped down the side of the chair, then scroll up quickly when OH goes over to him and lies that he's done a whole exam paper.  OH checked once after prompting from me and he produced something which he didn't do, OH fell for it made it clear poor little SK was a good boy and I wasn't being helpful by insinuating he was lying. So I do nothing now. The exams will be a disaster and BM and OH will run around trying to work out what on earth went wrong, my presence or something I've said or the time I asked him twice to empty the dishwasher will probably get the blame.

But stepping back, not engaging, and letting the SK's behaviour run its natural course until they fall so flat on their face / get arrested (wonder boy above is now breaking the law) / BPs wake up seems to be both the best protective course for us SPs and the route for the BPs to cut the denial and realise what is really going on with their children. You could also move out temporarily until you feel safe.

be getting a restraining order and skid is out of the house or i am out of the marriage. I wouldn’t even stay!!

death threats are not a funny thing, irrespective she is a teenager or young adult, threatening to kill someone purely because they are a stepparent is just total whacko

I wouldn't just tell H I was done, I would be moved out, living elsewhere, with phone number changed and restraining order in place. Really done! This is nothing to mess around with - this girl sounds truly disturbed and she has it out for you. Don't wait to see if some counseling works or her father figures out how to parent her. Get yourself out of this toxic, dangerous situation ASAP.

I have various issues with my 3skids and often hubby not address Things and giving up but shit i simply cannot imagine hubby allowing one of his kids with ex walking around videoing everything going on at home for evidence!! I mean that, because its such an invasion of privacy. Home is supposed to be your relaxing safe place, not where its “big brother” reality tv show and she makes death threats... thats just disturbing and all hubby does is send her to his parents instead of addressing her issues. 

The fact you have other kids (bios) at home, does hubby not feel guilty one bit how he’s actually allowing you to be in this situation in the first place?

also what others say about gut feelings and if its just all talk or write in a book but they’ll never do it... i just want to say all those serial shooters at schools for example, they were the shy nerd who kept to himself, no one ever thought he was capable of killing but he did anyways. So just because she might write it in a book but may not appear to be capable of doing it doesn’t mean she isn’t capable of doing it.

death threats are serious and you should just be in defense mode and protect yourself and your son. Yes hubby will likely guilt the shit out of you but your simple response is “how can you even have the nerve or decency to let these serious death threats and invasion of privacy continue and not protect us from it 1 bit? Your attitude is just get over it, its nothing and you’re blowing it out of proportion... your kid has threatened to kill me several times in writing” then send him the screenshot of her death threats and state you should be getting a restraining order against her

if hubby’s attitude dorsn’t change and he dors not actively address this issue with no buts and make your safety paramount, he isn’t worth it

I think you should leave!

Like others have said make arrangements first then tell him you are gone.

It sounds like the girl is living in a fantasy world or playing out a role like on a tv show where the wronged child gets to bring the evil step to someking of 'Home Alone' type of justice. You are better than me, because whether she is just playing fantasy or not, I would never live in a house with someone who was actively planning on destroying me or my life to the point of constant documentation and CPS phone calls. No man is worth that drama.