I'm sorry to hear about your H being a royal jerk about this. I can just imagine how ugly it is right now. Try to stay calm, cool and collected (the 3 Cs!!!), and continue to legally work towards what you feel is best for your D in spite of what he does. I agree with Karen that courts are familiar with lying and exaggeration and they will see through any mudslinging. Eventually all this will be in the past and things will settle down. Just hang in there....
{{{{{hugs}}}}}}}
There is no arriving, ever. It is all a continual becoming.