Have you told the complaining resident that when she calls the police on her neighbor, and the Officer reports no noise violation, that she can be fined as a Nuisance Call herself? :) My curious nature would have to get the best of me at some point, and I would have to ask her why she has a problem with the "noise"? I have had residents who are older who tend to go to bed early and they complain about "noise" between the hours of 8:00 pm onward until morning. This is ridiculous by reasonable standards of living for almost everyone.
Now, that being said, I would try to isolate how the noises of children playing affect the neighbor's apartment. Perhaps it was the music playing that really bothered her and it was loud in the adjoining apartment. Oftentimes, that kind of noise cannot be heard outside the building or even at the front door, though it can be clearly heard in the neighbor's unit. She may have a valid complaint.
It may not be that she hates children or anyone, but simply is disturbed by the way the sound travels through the levels of the units.