Only in the book she read. Probably didn't happen when she reincarnated(though I'm just guessing). Plus if a random child came up to you and told you that you were their parent would you believe them without proof?
the emperor was looking for a boy (because he was told that it was a prince who was born) not a girl it was because of that he could not find before, but he secretly searches for his child for 6 years.
the emperor and the prince already rejected her and were cruel to a little child. fuck them, i love the dukes family already!