Really? In Egypt, خصام refers to not talking with someone because you're upset with them.خصام means "conflict" and has nothing to do with this.
That's how I heard it when I was in Egypt to... there was definitely that element of conflict.What I meant is that الخصام itself is not the conflict, but the result of it, i.e. they stopped talking with each other due to/after a conflict.
So we can use it in this context. A mother can tell her son: لو ما سمعتش الكلام حخاصمك = I won't talk with you. Not that this is the best translation for "give a time out", but I wanted to say that the word can work in this context, at least in Egyptian Arabic. I don't know about Syrian.