He's now following her, checking up on her, and I just found out that he threatened to hit her in the mouth. Is there something I can do to convince her of the seriousness of the situation beyond my gut feeling?
Unfortunately, both the young man and your daughter have been taught by movies and TV that when a man persists, it equals love. When a man is overly attentive, it equals love.
In a movie, if the leading man researches a woman's schedule, finds out where she lives and works, even goes to her work uninvited, it shows his commitment, and proves his love. When Robert Redford does this to Demi Moore in Indecent Proposal, it's adorable.
Stalking is how some men raise the stakes when a woman doesn't play according to his rules. It's a crime of power, control, and intimidation very similar to date rape. In fact, many cases of stalking could be described as extended rapes; they take away freedom, and they honor the desires of the man and disregard the wishes of the woman.
The stalker enforces our culture's cruelest rule, which is that women are not allowed to decide who will be in their lives.
I've successfully lobbied and testified for stalking laws in several states, but I would trade them all for a high-school class that would teach young men how to hear "no," and teach young women that it's all right to explicitly reject someone. The curriculum would also include strategies for getting away. Perhaps needless to say, the class would not be called "Letting Him Down Easy."
If the culture taught and then allowed women to explicitly reject and to say no, or if more women assumed that power early in every relationship, stalking cases would decline dramatically.
Looking for Mr. Right has taken on far greater significance than getting rid of Mr. Wrong, so women are not taught how to get out of relationships. That high-school class would stress the one rule that applies to all types of unwanted pursuits: Do not negotiate. And that's my guidance here: "Don't negotiate." Your daughter will benefit greatly if she exercises the ability to get out of a bad relationship -- as you clearly know. (There's much more information on this topic in my books The Gift of Fear, and information specifically written for teenage girls in Protecting The Gift.)