I wonder what people think happens when they say this. Where exactly do you think it is "logged" and what is the point of "logging" it, exactly? Do you think there's a big notebook called "stories about nasty people -use this as evidence of poor character if someone is arrested for a different crime despite it not being investigated or evidenced so is pure hearsay and gossip"?
If you ring the police to tell them something happened but you don't want them to do anything about it, you at wasting police time. it is of no more relevance to them than if you call to tell them about a nice rainbow or cute puppy you saw that day, but is tying up their call handlers and preventing them from helping people trying to report an actual crime.
Not to mention once a crime is reported it isn't the victim who makes the decision whether to proced with investigation or not. It doesn't matter how much a victim or witnesses "presses," the decision to charge is not make by them, and should be made on an evidential basis not solely on the victims feelings.
Although their wishes should be taken into consideration, cases can be, and are, brought to court without the victim wanting them to be.
Honestly with borderline crimes like this, if someone else reported it and Op's dd didn't want to engage then it probably wouldnt meet the threshold for investigation/charging - but it could. With lots of witnesses they don't need the Dd's account- although if they did decide there was enough to charge and it got to court stage they can get a warrant to force her to attend even if she didn't want to -including being charged herself with obstructing the course of justice! Is this uncommon, and fairly unlikely in these specific circumstances- yes, but not impossible.
Do not tell the police about a potential crime if you do not want it to be investigated and potentially considered through the full legal process, because once you do the decision is out of your hands.
I'm glad the OP is ignoring all the people who don't have a clue and not setting those wheels in motion by "reporting to police". Legal proceedings are no joke. They are stressful and intimidating. With the delay in listing cases it could be hanging over her dd's head for years before it's heard- only to be dismissed on a technicality. You've seen the sentences or lack thereof hardened criminals get - a slap on the face is not going to get her imprisoned! I know a pp said in similar circumstances it intimidated the girls who had hit her but if this girl is that unhinged it could equally piss her off to the extent she makes the whole family's lives a misery.
It would be completely unfair and irresponsible for OP to do anything on her ADULT child's behalf without them wanting to. How would you like it if you moaned to your husband about someone at work doing something to annoy you, and he called up your boss behind your back to tell them to discipline the colleague because he knows better than you? The dd is an adult, OP and her dad can offer advice but it is weird and paternalistic to do anything else without her consent.