Is it true that the Prophet, may God’s prayers and peace be upon him, said: “There will come a time upon my Ummah when a father will wish his son were a dog due to his disobedience”?

There is no text with this exact wording in the books of the Sunnah. However, some narrations mention similar meanings, among which is what Ibn al-Jawzi mentioned: "For one of you to raise a puppy is better than for him to raise a child in that time." This hadith is fabricated and unsound. These reports should not be relied upon, as they pertain to matters of the unseen about which nothing has been authenticated.