What will happen is that your alumni parent will get a congratulatory letter which is the start of their personal acceptance process should the unthinkable happen and you not get admitted.
At Stanford, what legacy applicants get is a second read of their essay to make sure both evaluators agree.
According to last year’s statistics only 16% of legacy applicants were accepted…which means 84% are rejected. Your mom having worked in the police dept will have no bearing whatsoever. On the other hand, if she was a Stanford faculty member in good standing (presently) that would be considered a major hook…much more powerful than being a legacy!