Yevamot 101 - Details of paternity
In the previous case of uncertain paternity , what are the circumstances? If both men were Kohanim, one would be marrying a divorcee and his child would loose his status of a Kohen, so he would be allowed to go to a cemetery. Since the ruling prohibits this, it cannot be talking about not waiting after a regular divorce.
In the same vein, the Talmud excludes all other cases and is left with one: she lived with each man without any legal framework, had a child from one of them, and the term "husband" was not meant literally but only for the clean language. Incidentally, if this child strikes both husbands, he is not punished, because we don't know who the real father is, thus cannot give him a proper warning, and punishment does not exist without a warning.
Now for the mitzvah of chalitzah. The woman recites the verses about the brother not wishing to "establish his brother's house," the man confirms that he does not want to marry her, then she removes his shoe, spits toward him, and recites "so it will be done to a man who will not build his brother's house."
Art: Waiting For Father's Return by Philippe Lodowyck Jacob Sadee