What is the expiation for saying, "You are unlawful to me if you do not sleep at your parents' house," with the sole intention of threatening and punishing, and her not sleeping at her parents' house? And does delaying the expiation make what occurred before it fornication?

What you uttered is a declaration prohibiting your wife from staying overnight at her family's home; if she does not stay there, you have broken your oath. The prohibition of one's wife depends on the husband's intention. If you did not intend divorce or ẓihār by it, but merely a threat, then an expiation for a broken oath (kaffārat yamīn) is incumbent upon you. There is no harm in approaching your wife before performing the expiation, as it is ẓihār that prohibits approaching one's wife before expiation. One should be cautious about being lenient with words of prohibition and divorce.