For me it would just depend on my child, the situation, the history, what responses I had tried, etc.
Sometimes just knowing that it's okay to let go of your frustration allows you to do just that, and find new depths of creativity. Sometimes you really have hit an absolute personal limit and the best thing for everyone is a clear, definite boundary to acknowledge it. There is such a balance in all of this!
Have you sat down as mamaduck described and really gone over the meaning of the word hate? I'm guessing you probably did. I like sledg's "One, two" approach of diffusing strong emotions in the moment, and waiting until emotions are calm to discuss your expectations.
But I'm not getting the impression that your children *are* expression strong emotions. Or am I reading it wrong? It sounds like they are using this word like a habit, not being especially hysterical or angry when they use it.
If I felt my child had made a *habit* of the word "hate" (meaning, it wasn't that he was overwhelmed with anger, but a habitual behavior to express general disagreement and disappointment), I would reach a point where I would feel it was up to me as the parent to help him succeed in using better language consistently.
I think I'd approach this as not being about me personally, but about my child having picked up some very poor language skills. Like if my child had picked up chronic whining, or something like that. In my experience brainstorming together, and then implementing the plan created, can be very helpful.
Now this is what would have worked with my ds: Creating a plan together beforehand. For example, we might decide that if he fell back on using the word hate, I would "freeze", until he said he wanted a do-over. A do-over would mean that he got an immediate chance to try again using better words. So let's say I'm reading to him, and I get sleepy, and say that I need the story to end on this chapter. And ds is disappointed and says 'I hate you!'. I'd "freeze" on that note, say nothing further, and continue on with my evening. My own ds would have *immediately* wanted conversation back, which is why this would be the likely plan we'd create. For him my "Freezing" conversation would have been very helpful--none of the embarrassment of being told outright to use other words, no heated emotional response from me, nor any criticism. But also a very clear demonstration for him that the word was a poor choice, and a motivation to make a better choice quickly. I can see him saying 'I want a do-over!'. Me saying "Okay, great. I said I was sleepy, and needed to end on this chapter. What words could you use instead of hate?". Then help him pick something different, and then lots of good vibes to reinforce the better choice. Lots of praise for making the better choice.
For *my* ds this probably would probably be a quick and positive exercise that would help him tremendously getting in touch with his own better skills--but I can't anticipate all the ways it might backfire with another child. The overall point is that if you step back and take in all the things you know about your child, and get clear on what your goal is in addressing this issue...can you create some idea's from there? If so can you involve them in conversation to create a plan from your intuitive idea's? Can you see that working?