Regarding the Hadeeth of Fatimah
In explanation of the hadeeth narrated by Al-Miswar bin Makhrama:
"I heard Allah's Apostle who was on the pulpit, saying, 'Banu Hisham bin Al-Mughira have requested me to allow them to marry their daughter to Ali bin Abu Talib, but I don't give permission, and will not give permission unless 'Ali bin Abi Talib divorces my daughter in order to marry their daughter, because Fatima is a part of my body, and I hate what she hates to see, and what hurts her, hurts me.'" [Saheeh al-Bukhaari, Vol. 7, Book 62 (Book of Marriage), Hadeeth No. 4887]
Narrated from Ali ibn al-Husayn:
"Ali demanded the hand of the daughter of Abu Jahl. Fatimah heard of this and went to Allah's Messenger saying, 'Your people think that you do not become angry for the sake of your daughters as `Ali now is going to marry the daughter of Abu Jahl.'
On that, the Messenger got up and after his recitation of Tashahud (witnessing the oneness of the Creator and the prophethood of His Final Messenger) I heard him saying, 'I married one of my daughters (Zainab) to Abu Al-`Aas ibn Ar-Rabi` before Islam and he proved truthful in whatever he said to me. No doubt Fatimah is part of me; I hate to see her troubled. By Allah, the daughter of Allah's Messenger and the daughter of Allah's enemy cannot be the wives of one man.'" [Saheeh al-Bukhaari, Vol. 4, Book 53 (Book of One-Fifth of War Booty), Hadeeth No. 2900]
This hadith talks about the incident of `Ali wanting to marry the daughter of Abu Jahl, the bitterest enemy of Allah and His Messenger. Abu Jahl remained a kaafir 'til his death. He humiliated the Prophet and his Companions and tortured them; he also attempted the life of the Prophet many times.
Abu Jahl was finally killed by the Believers in the Battle of Badr long before `Ali proposed to marry his daughter. Thus, it becomes evident that the Prophet's justification of his disapproval of that marriage was not because he discouraged polygyny, as he himself was the best of examples and had multiple wives, but because of the shameful family history of the bride, which would definitely trouble his beloved daughter.