I can use child to replace son or daughter, sibling for sister or brother, and parent for mother or father.
What is the unisex replacement for fiancée and fiancé?
I don’t need it for speech, but for formal or semi-formal writing.
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For formal writing, betrothed would be my number one choice. But, as Lunatik already gave that answer, I'll provide some more: spouse-to-be (instead of the gender-specific wife-to-be and husband-to-be), future spouse, prospective spouse, intended (date and informal).
Of course, it's much easier to refer to use adjectives and refer to the couple as a whole, if you can rewrite it in this way. This opens the door to: engaged, affianced, pledged in marriage, etc.
Traditionally, "fiancé" was used male and "fiancée" for female; however, this is not reliably followed today, and "fiancé" is often used as a gender-neutral term.
Matt called his fiancé and told her to come to the office.
-- 2018, T. K. Kohl, Quest of the Staff and the Sword, page 153.