Record and document everything . Seek legal advice.
What she is doing is wrong I feel your pain my ex speaks poorly off me aswell I front off my kids.
She has gone as far telling my oldest boy that I never wanted him and found him to be an inconvenience. 
My oldest son has not talked to me now in almost 2yrs.

   

I ran into the same thing with my case there was an onslaught of aligations in the court paperwork from my sons mother 
You CANNOT allow this to go unchecked or unchallenged ...if you the court will accept it into the court record as fact 

The only thing you can do is what I had to do 

Stand up and say where are the police reports, cas reports, and doctors reports to back this up? 

It's nothing more than an underhanded tactic to frustrate the court process and alienate the father by means of a smear campaign

If there's no professional reports to back up these claims they need to be ignored by the court and excused from the record 

Hope it helps 
Keep fighting brother 
Together we can stop the war on dads

   

You need a good family law lawyer and a detailed written put parenting plan showing how you care and provide ALL the child's needs. Bed, food, clothes, education, socializing, and even time with the other parent. Show how responsible you are. Rise above her hatred. The one who screams the loudest loses.

   

U can request a Parental fitness assessment through Court. It may cost you but these professionals are amazing!