I want to first say how sorry I am to read about this horrible, I mean indescribable horrible incident that you went through today. No one, and I mean no one should have to endure that. For him to do that in front of your children, I don't even have the right words. There aren't any words.
I know this is probably not what you want to hear right now but I think it needs to be said and is very important. I think the first thing you should have done when you left the parking lot was drive straight to the police station and report every single thing that happened. After my ex lied about me the way yours did, my lawyer and the police told me to come straight to the police station and report something right away every time it happened. They now believe me instead of him and brought him up on charges of criminal harassment. I think in this situation especially it would have been beneficial to go right at that moment while your eyes were still red from crying and while your girls were still upset. It is not a lot of proof but it is definitely some, of what you had been through. This is especially important if he is making threats to falsely accuse you again like he did the last time. You need to get ahead of it so that he will no longer have that kind of power over you and will never be able to do that again. I know in the moment the first thought is to want to run, get away and go somewhere safe to calm down but it is better to get it all on record, every single thing. I am thinking you should think about calling the police now and making the report. One of the things they asked me when I waited was why did I wait to report it. Please consider it.
Wishing you some peace tonight.