The problem is that I’m guessing this mom is getting questions and looks every time she goes out with her daughter.
The SW staff could have just as easily pulled the names on their tickets- which you’d have to have ID to get, anyhow- as checked their ID. The cops could have done that as well. Including pulling up her id in the DMV database they have access to. “yup. that’s her.”
The cops could very easily have just pulled the mom’s ID off DMV, looking at the information supplied to buy her ticket. That’ll get them to her on the DMV. If her ID is valid, it won’t offer any more information than is on the DMV, and there’s really no way to prove they’re your kid at all.
One of the reason I keep old photos (and new) of my niece and nephew- especially photos of me with them- is so to show cops when I get them called on me for being a single man doing “mom”-things at the park. Dealing with cops because you don’t fit some karen’s idea of who should be taking kids to a park gets old very fast.
And to be perfectly blunt, “you should just be grateful we care” is incredibly ignorant; and the staffer was probably just following protocol. but the reason they did it was fundamentally rooted in racism.