The anti-islamists allege the following:
"He too harassed and mocked Muhammad in Mecca and wrote derogatory verses about him. He too was captured during the Battle of Badr, and Muhammad ordered him to be executed. "But who will look after my children, O Muhammad?" Uqba cried with anguish. "Hell," retorted the prophet coldly. Then the sword of one of his followers cut through Uqba’s neck.
Source: Bukhari, vol. 4, no. 2934; Muslim, vol. 3, nos. 4422, 4424; Ibn Ishaq, p. 308 / 458. Bukhari and Muslim are reliable collectors and editors of the hadith (words and deeds of Muhammad outside of the Quran). These three passages from the hadith depict Muhammad calling on Allah for revenge on this poet"
Again they fail to mentioned that Uqba bin Abu Muayt, was a person who once tried to kill the Holy Prophet, and such was a constant and open threat. This was a deadly serious threat which was further confirmed by the fact that he also joined the army against the Muslims at the Battle of Badr
Observe the account on his attempt to kill the Prophet:
SAHIH BUKHARI, BOOK 60: Prophetic Commentary on the Qur'an (Tafseer of the Prophet (pbuh))
Volume 6, Book 60, Number 339:
Narrated Urwa bin Az-Zubair:
I asked 'Abdullah bin 'Amr bin Al-'As to inform me of the worst thing the pagans had done to Allah's Apostle. He said: "While Allah's Apostle was praying in the courtyard of the ka'ba, 'Uqba bin Abi Mu'ait came and seized Allah's Apostle by the shoulder and twisted his garment round his neck and throttled him severely. Abu Bakr came and seized 'Uqba's shoulder and threw him away from Allah's Apostle and said, "Would you kill a man because he says: 'My Lord is Allah,' and has come to you with clear Signs from your Lord?" (40.28)
The above hadith, shows Uqba as dangerous hostile, an extremely intolerant person of the Holy Prophet (S). So much so that he even attempted to kill him, and took up arms against him. Now, I looked all over the collection of Hadiths, to find a narration that says the Holy Prophet (S) told Uqba that hell will look after his children, and I couldn't find a single narration that says that.
Also, if this story is to be found in the works of Ibn Ishaq, then it must be noted that the books on Rijal, have explicitly stated that Ibn Ishaq used to borrow from unreliable sources in regard to the battles of the Holy Prophet (S). (See Sirat Un Nabi Vol. II p. 173 by Allama Shibli Nu'Mani)