None of the information you've listed as being checked by her is private, nor would it be included in something like an NCIC check. DL information, marriage and divorce information, birth records, and much more is easily and readily available to anyone who knows who to ask for it, or via several hundred different companies who'll do the leg work for a fee.
You can certainly file a complaint with her employer, but most law enforcement employers won't be upset that a law enforcement employee is checking up on people they date - so long as they aren't using closed systems to do so (NCIC being the big no-no, and if you've no arrest record, NCIC wouldn't HAVE a record on you). Many agencies would actually approve of such vigilance, since a HUGE portion of "problems" that lead to law enforcement personnel loosing their jobs comes from things that happen in contexts OTHER than at work.

