How old are you and your wife? This kid is 18 if I'm reading right. Harrassment is all about perception, never about intention. If your wife feels harrassed (i.e. she perceives this as harrassment), then it is her responsibility to raise the issue to her company's HR department and determine the best path forward.
To me it sounds like a young 18 year old kid acting like, well, an 18 year old kid. He probably doesn't know how the world works and what is and is not acceptable on the job. In the end, the ball is in your wife's court as to how this is handled. You getting involved will most likely produce no good outcome and considering you have kids, it's not worth the risk. My guess is your wife sees this as harmless since the kid is so young, a raging hormones type thing. Your wife has three children that I assume she loves dearly and would never think of turning their world upside down for some 18 year old nobody, and that's assuming she has no feelings for you, which I'm sure she does since you're married to one another.
If I were her I'd sit down with the kid one on one and gently tell him that the way he is acting on the job, while flattering, could be viewed as harrassment since she is a married woman with children, and that he needs to be more careful, and that she would appreciate it if he would refrain from such behaviors toward her in the future. After doing so she should inform HR so that they can make a note of it in the kid's employment file. In most cases were your wife to go to HR beforehand, they would guage how comfortable she was confronting him like this and if she felt comfortable they would recommend doing what I just described above first. A note would be placed into the kid's employment record but assuming no further incidents occurred it would never go any further from an HR perspective. It's all about documentation/evidence from an HR perspective, a paper trail is necessary. If your wife is hesitant, I would say to her that he's more likely to treat not only her but also other women this same way in the future if she doesn't choose to nip it in the bud now. Just MHO as a manager who's had to deal directly with these types of issues as part of my job. Too often people make the mistake of trying to deal with these very sensitive issues without HR's involvement and almost without exception it comes back to bite them in the a$$ later. If it's a small company and no HR dept exists, well, that's a different story, I'd just try and have the direct one on one with the kid to make him aware that he needs to tone down his behavior, for his own career's future.
