Unfortunately, there is absolutely no risk of jail time if a women makes false abuse allegation (either abuse towards her or towards the kids). On the other hand it is a common practice advised by unscrupulous lawyers to get rid of the dad and get full custody by getting a temporary restraining order (it is called the "silver bullet").
A recent story where it happened to a dad, who eventually got killed by the father in law : https://www.youtube.com/watch?v=H_z0AfxT2bE No coverage or sympathy from either the media or the politics.
An entire industry exists just to bleed families dry by getting women to claim abuse (mental abuse is enough) to get the kids, 1/2 the man's stuff and a steady income. The entire "civil court" legal system is broken in the US. It is what Trump specialized in, civil court cases just to fu*k with people and bully them into getting what he wanted.