What a friggin nightmare! I am so sorry you are having to deal with all of this. I don't know what state you are in, but in the court system here, children's wishes about which parent they want to live with are taken into account around the age of 12, and as early as 10 if the child shows the maturity to make the decision.
As everyone has said, document EVERYTHING! I have an excel spread sheet with dates, times, quotes, etc. Even if it seems small or like something you will be able to remember later, write it down anyway. I am almost 4 years out, and am surprised when I look back at old notes. Trauma makes a mess of our memories. It sounds like you are doing well at keeping screenshots and the like...well done!
Also another vote for getting to a women's shelter for assistance. The folks at my local one were an invaluable resource. I never would have thought of myself as the type of woman that would need to avail myself of their services, but am so grateful that something let my pride go enough to seek help. There is no shame in needing help, and you don't have to have 2 black eyes and a broken arm to go.
Also, please consider a counselor for your children. Not only will it help them, but will be a "professional" opinion to help offset the allegations of you as the crazy ex. I have been accused by XWS of being paranoid. DD's counselor has said XWS is never to be alone with DD. It really helps me feel like she is in my corner, and I am not crazy. It also shows you are concerned about the well being of your children.
One last thought. Just IMHO, please behave yourself as if you are in a court of law anytime you have any dealings with him. Do not do anything or put anything in writing that you would not want to repeat to a judge. Sounds silly, but it has been one piece of advice that has served me well over these last years. Keep all communications to text or email so there is a record, and limit communication to kids and finances. Again, nothing in writing that you would not read to a judge in a court of law.
I have no idea what your guy is capable of or how serious he is about his threats, but I can tell you that mine made all kinds of threats in the early days. They were all empty. He was just squirming in his shame and projecting all of his crap on me. Twisting in the wind as it were.
Please stay strong for your kiddos. This can be more of a marathon than a sprint, so please try to find time to take care of yourself. They need you!!
And please stay close here. You have found an amazing group of kind, compassionate, and wise folks. "If you marry a chicken, don't expect an eagle."
I don't know if my chicken will ever become an eagle. But rest assured, I'm going to be a phoenix. Nevermind that I am still in the ashes stage of the process.