Is there anything in the US laws against using swearing and abusive language openly in the public - here where I live such a behaviour, depending on other circumstances, might be seen as a petty offence, and children being at the scene make up for an aggravated offence. If not that, then maybe Your local equivalent of Orphan's court might be "happy" to learn about this, especially, if You have a video proof. Or those cameras in front of the police precinct have taped that already - I am sure in the US there must be video surveillance outside the police premises, but but they might share those records only on the basis of warrant, plus there might not be an audio, besides usually this stuff gets stored for 24-48h only and then the new record erases the previous one.
Again, this is not a legal advice, and comes from someone who is familiar with the European systems - I can only provide basic guidance on how to collect evidence and where to look for them, so if You want to move forward with this, contact a local lawyer for legal assistance. Maybe just a bit of emotional blackmail or simple bluffing might suffice - like telling them that You already have recorded that or have a tape with it...
Take care and be safe