All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
First of all, we will say that ‘Ikrimah ibn Abu Jahl remained as a Muslim since he embraced Islam and did not apostate after the death of the Prophet as you claimed.
Rather, he took part with other honorable companions in fighting against those who apostated.
Ibn Hajar said in Al-Isaabah:
“Abu Bakr sent him [i.e. ‘Ikrimah] to fight the army of Nu’maan, and he defeated them, then he sent him to Yemen, and after he came back, he went out in Jihad in the year when he died and he died as a martyr...”
The fact that his father was Abu Jahl does not harm him at all as long as he embraced Islam and died as a Muslim. Indeed, Allah clarified to us in His Book that a Muslim being a relative of a non-Muslim does not harm him; in the same way that a non-Muslim having a Muslim relative does not benefit him.
Allah Says (what means): {And Allah presents an example of those who believed: the wife of Pharaoh, when she said, “My Lord, build for me near You a house in Paradise and save me from Pharaoh and his deeds and save me from the wrongdoing people.”.} [Quran 66:11]
Ibn al-Qayyim said about the interpretation of this verse:
“The example: is when a believer has a (blood) relation with a non-Muslim, then this does not harm him in anything if he is not in conformity with him in disbelief and deeds. Also, the disobedience of others does not harm the obedient believer in anything in the Hereafter, even if he is harmed in this world because of the punishment that is inflicted on the people of the earth, if they abandoned the command of Allah; so the punishment is general. Pharaoh's wife was not harmed because she had a relation with him while he was the most evil disbeliever. On the contrary, the wife of Noah and the wife of Lot did not benefit because of having a [marital] relation with them though they were Messengers of Allah, the Lord of the worlds.” [End of quote]
As for the story of the Prophet marriage to Qateelah bint Qays, the sister of al-Ash'ath ibn Qays, then the Prophet concluded the marriage contract with her but he died before he consummated the marriage with her, and before he even saw her.
Ibn Hajar said in al-Isaabah:
“The Messenger of Allah married her [i.e. concluded the marriage contract with her] in year 10 A.H, but he died before she was brought to him as a bride, and he neither saw her nor consummated the marriage with her….”[End of quote]
Therefore, she was not among the wives with whom he consummated the marriage with them, and whom the believers are forbidden from marrying, according to the agreement of the scholars.
It is for this reason that Abu Bakr wanted to punish ‘Ikrimah for getting married with her but ‘Umar told him that she was not among the mothers of the believers, and that the Prophet did not consummate the marriage with her or command her to wear the Hijaab [like all other Prophet’s wives]. Rather, ‘Urwa ibn az-Zubayr, himself denied that she ever married the Prophet and said: “The Prophet did not marry Qateelah bint Qays, nor did he marry Kanadiyyah except the sister of Beni al-Joon, whom his right hand possessed, and she was brought to him (as a bride) but when he looked at her, he did not like her, so he divorced her and did not consummate the marriage with her.” [End of quote]
Allah knows best.