My friend used to compete at ice dance and had a heated relationship with her partner! Sometimes he would deliberately have his hand/arm positioned wrong so she couldn't grab it, or drop her, and she once kicked him in the head (i think partly by accident!)
Same friend also got kicked off the ice by her coach for kicking the ice in frustration.
BTW, she's very lovely and not a violent person (anymore...)
I think asking skaters who repeatedly take out their frustration by kicking the ice to leave the ice (either for the rest of the session or for a set time out period) is a really good idea. The ice is for training, vent someplace else (where you're not making dents in the ice for other people to fall in!).
But violence towards people (skaters, coaches, bystanders) is a big NO-NO! There is no excuse for it. Kids should be taught better ways of handling anger and frustration and adults should know better!
Rinks should be able to ban a skater from all sessions. Clubs who run patch ice should be able to ban a skater from their sessions. In practice, I'm not sure how this would work, as from what I understand, ice monitors are volunteers and shouldn't have to face a potentially violent confrontation if they ask someone to leave the ice (I used to work in a shop and if the manager wasn't around to provide backup, we wouldn't challenge a group of well known shoplifters if we saw them in the act, it wasn't worth the hassel!). At my rink, it would probably be the head coach's responsibility to "police" the situation.