What if a person filed a false police report about me resulting in my arrest. But the next day admitted why she did it over a recorded phone call through a county jail telephone, resulting in the charges being dropped? Because that was also done to me by my child's mother. This one person has caused me more pain and anguish then anyone else I've met in my life combined.
Reports to the police are also
privileged but the privilege that covers police reports are conditional or qualified, which means that the privilege can be defeated upon a showing of actual malice. If a report can be shown to have been made by a person who
knew it was false at the time it was made and the report can be shown to have been made with an intent to cause harm, then the report can lead to a criminal charge. But false reports rarely result in criminal charges, for a variety of reasons.
If the person who filed a false report to the police later recanted or admitted to lying, the police will decide to pursue the matter (or not).
I am sorry your child's mother is causing you so much pain and anguish. This happens when relationships go sour and perhaps happens even more frequently when a child is part of the equation.
Again, seek out the help of a family law attorney in your area. The attorney can help you address the issues you are having with your child's mom.
For custody and related questions, by the way, you might be best off on this forum by posting those questions in the Family Law section of the forum. I know forum members can locate you here in Defamation - but I am not seeing that you have any defamation claims worth pursuing (based on what you have posted) and it sounds to me as if you could use some concentrated advice on handling the problems with child custody.
I just saw your additional question and the answer to it is that, yes, you can sometimes find attorneys willing to work with you on a part time, as needed, hourly rate basis. You will probably have to call around a bit.
Good luck.