As for your claim that the other chain of transmission contains an addition—namely, that he instructed him to divorce her once, and that a divorced woman must observe a waiting period—this is not an addition. Rather, unless “a single divorce” here means an annulment, this narration contradicts the other one. The other narration explicitly states that she should return to her family after one menstrual period. Even if it contained only the words:
“He instructed her to observe a waiting period of one menstrual period,”
this would clearly mean that he instructed her to observe one menstrual period, not more. Had he instructed her to observe three, it would not have been permissible to report only that “he instructed her to observe one menstrual period.” How much clearer, then, when it also says, “and return to her family”!
Moreover, all the narrations transmitted through the other chains support or agree with this. They are further supported by the practice of 'Uthmān ibn 'Affān, one of the Rightly Guided Caliphs. Some chains of transmission for the report concerning him have already been cited, along with the fact that, in this matter, he followed the Sunnah concerning the wife of Thābit ibn Qays.
Furthermore, even supposing that the other narration stated, “He instructed her to observe a waiting period of three menstrual periods,” this would constitute a conflict between the narrations, requiring consideration of which of the two chains was more authentic. How, then, can that be claimed when it contains only the words, “And divorce her once”? Those who transmit this are Ibn 'Abbās and his companion, both of whom also narrate that “he instructed her to observe a waiting period of one menstrual period.” Both also hold that khul' is a release obtained by compensation and does not count toward the three divorces.
As for the words, “And divorce her once,” if this wording, together with what precedes it, is reliably preserved as the words of the Prophet, peace and blessings be upon him, then one of two explanations must apply: either it must be said that divorce