Typical of Western Culture. Unfortunately, there is little you can do now that the courts are involved.
If the courts don't work for her immediately then expect the situation to escalate.
Record all phone calls, keep all correspondence, make regular videos of meetings, and make sure to have witnesses to every interaction you have with the mother.
Expect the following:
False allegations of DV.
False allegations of sexual abuse.
Overinflated child support payments that will not be lowered even if you lose your job or have to go to a lesser paying one.
Parental alienation (if she cannot turn the courts against you, then she will turn the child)
Most men think these things can't happen to them. They suffer the "not my ex" syndrome, and learn a little too late. Protect yourself and your child by fighting tooth, claw, and nail for every ounce of time you can get with him. You must establish a a living pattern that is conducive to child-rearing....and expect local agencies to regularly investigate your home to make sure that it is a suitable environment for the child to stay (even if only one night a week).
Do not speak badly about the mother in front of the child. Those types of things will inevitably get back to the mother, and she will be able to claim "emotional abuse" under the DV umbrella that has been enshrined in law.
Do no have roommates, including other women. These roomates also provide convenient targets for false allegations.
Do not trust this woman at all. It is not in the interests of the child or yourself to ever trust an individual who has state power on her side automatically. There are too many cases of the abuse of protection orders to even consider it.