The correct path of action would be, if you have children, to have the correct kind of lawyer on retainer already. This is the unfortunately reality we have.

You do not speak with the police, you calmly but firmly inform them that they can return with a warrant if they think there is something actionable.

You then proceed legal action against the false reporter. Sometimes all you can get is a no contact order, sometimes you can get a stalking injunction, sometimes a full blown restraining order. This is why you want a lawyer ahead of time, they know how to deal with this.