"Once Hazrat Abdullah bin Umar (RA) was playing with Hazrat Imam Hassan and Hazrat Imam Hussain (RA). At that time Hazrat Imam Hassan (RA) passed a remark on Hazrat Abdullah bin Umar (RA) calling him the son of his slave. Hazrat Abdullah bin Umar (RA), went back home crying and when asked by Hazrat Umar (RA), narrated the whole story. Hazrat Umar (RA) started crying and asked his son to go back to Hazrat Imam Hassan (RA) and request him to write these same words for Hazrat Umar (RA) as a token of authentication to be placed in his coffin."
This statement if not meant as a metaphor is certainly wrong for at least two reasons one of them the difference of age between 'Abdullah ibn' Umar () and al-Hassan (and al-Hussain) ibn 'Ali() as pointed at by @TheZ. This simply nullifies the possibility that they played together.
Secondly the fact that his mother and the mother of his sister Hafsah () the mother of believers was a free woman and sister of the sahabi O'thman ibn Madh'oon (Mad'uwn) () and the same applies to his father.
You may find this quoted here in the Wikipedia site about him and here in the Wikipedia site about his mother Zaynab bint Madh'uwn which confirms that she is from among the clans of Quraish (Jumah). She accepted Islam however it is unclear whether she witnessed the hijrah or not. As some historian pretended she went to Medina while others say she didn't.
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