Whenever she does not get what she wants, my 3 years old daughter would say that we don't love her. What should I do to discipline her? I do not want to spoil her.

This phrase is all kids favourite. I think they somehow become so smart at such tender age to know when to use it and how. Kids do not mean it of course but don't know how they know that it hurts the most. I think whenever she says this ask her why does she think so, and if she is smart enough to use this phrase at 3, then I think then you can give her references from the previous days when you got her favourite thing she demanded. Or, you can tell her that everything that we desire cannot happen, and then you can again site some examples of her cousins, when they had asked for something from their parents and they were not allowed to have that. You can also narrate incidents from your childhood, and how you also did the same things as her. I do the same with my daughter and in the middle of crying she bursts into laughter. I think, when her mood is fine, communicate with her a lot and tell her examples having you, her father and cousins as the main characters.