I'm sorry you're going through this
I have a 4 yr old daughter as well, I just keep saying that daddy has some problems and is sick and only he can fix them and that is why he is mean sometimes or lies. She seems to understand since she has seen him change from a great dad to what he is now in a short period of time. i wonder if she goes to therapy and they put in their report that him saying things that are harmful to her emotional well-being they can maybe court order parenting classes or something?