I HATE YOU!
It is very likely you will hear this pop out of your precious little ones mouth one day.
Do they really hate you? I'm going to guess no. They might hate that they have to obey, or hate that you are making them do something they don't want to do, but they don't hate you.
The way I always handled that was to not react. "Oh, I'm sorry you feel that way." and move on. It's suppose to cause a reaction and if you don't react they won't keep doing it. Once things have calmed down though definitely tell them you are disappointed for using ugly words when they were upset. Give them better words to use like "I'm very mad!" or "This makes me grouchy!" which are acceptable.
So far, I haven't been told anyone hates me... but I think my days are numbered with Mason. He told me the other day that "You are making me have a really bad day and I hate this day because of you" He also uninvited me to his birthday party because I wouldn't buy him a new toy. So there ya go.