None of which is illegal.
I highly doubt this subjective enhancement of the tale by the police is true or worth the ink it took to write it.
Besides, what kind of mother isn't first worried about a DYFS person threatening to take her kid from the house.
Knowing NJ, this is CYA by the cops--they know they stepped in it bigtime, and need to justify what they did, as they are not used to any kind of resistance--especially the legal resistance shouted at them by the lawyer on the phone.
This is precisely why you don't say anything to cops without a lawyer present. Whatever you say, even innocently, can and WILL be used against you.
If I faced a similar situation, with cops and affirmative action “child services” mice beating down my door and demanding to see my gun safe, I’d be “ranting, WTF!”, too.