Is saying "I don't do that" in response to advice to treat one's wife as the Prophet treated his wives considered an act of disbelief (kufr)? What is the repentance for it? Are there any worldly consequences, such as the annulment of the marriage contract?

What is mentioned in the question represents a lack of adab (proper conduct) towards the Prophet (peace be upon him) and towards one's mother. A Muslim must be careful in their speech regarding the Prophet (peace be upon him), for Allah Almighty says: "Do not make [your] calling of the Messenger among yourselves as your calling of one another," and "That you [believers] may believe in Allah and His Messenger and honor him and venerate him." It appears that the questioner did not intend disrespect, but rather wished to express his inability to emulate the Prophet in forbearance and forgiveness, and this is not disbelief, though it is a mistake. The questioner should seek forgiveness and improve his choice of words, striving to obey the Prophet's command: "Whoever believes in Allah and the Last Day, let him speak good or remain silent."