I was going to post on a slighly different tack to Iggly: given that she is already nearly 3 years old, I don't think you have to assume that anything she comes up with has been taught by you. At that age, my dd was quite capable of using her own brain to draw her own annoying conclusions and act upon them. This is a conversation dd and I had when she was 2 (and I had clearly managed to get up her nose- cannot remember what I had done wrong):
dd: I don't love you any more, I don't want you for a mummy
me: well, that's a pity, but I still love you and I will always be your mummy
dd: not when I'm grown up
me: yes, even when you're grown up. You may go to live in your own house and you may have a family of your own, but I will still be your mummy and I will still love you
dd (with triumphant calm): no, you'll be dead then
me (muttering under my breath): don't you bank on it, my dear, don't you bank on it...
May I add that dd is now 15 and we have a very good relationship indeed. And that she has never heard me or dh say that we do not love anyone, or seen us withold love as a punishment.
It was not emotional blackmail; it was simply emotional immaturity. She was trying to punish me, no doubt, but not in the dreadful way of somebody old enough to understand what the concept of death and losing a parent means.