That’s true he did compose satrical verses against the Prophet (saw) Once he realised that his childhood friend had overcome all his adversaries so must the Prophet of Allah headed to meet the Prophet (saw) who was on his way to conquer Makkah. He took his young son along with him to soften Prophet (saw)'s feelings towards him.
For three days he lost no opportunity to keep himself along with his young son within Prophet (saw)'s eyesight. After 3 days of purposefully ignoring him the Blessed Prophet (saw) relented saying: "Ya Abu Sufyan, what kept you away for so long? Ya Abu Sufyan, why so much delay? Ya Abu Sufyan, what kept yoy away from the truth? (sorry no reference - but I remember it well having once read it)
Yes, he is Prophet cousin and his full name is Abu Sufyan b. Harith b. 'Abd al-Muttalib
Sahih Muslim, KITAB AL-JIHAD WA’L-SIYAR see hadith Number 4385