This discrepancy does no harm, for ʿUrwah and ʿAmrah are both reliable narrators well known for transmitting from ʿAʾishah—may Allah be pleased with her.
Al-Hakim’s narration (1/144–145)—from whom al-Bayhaqi also narrated it (1/31)—is anomalous, for he gave it through the route: ʿUrwah, from ʿAmrah, from ʿAʾishah, attributed to the Prophet, peace and blessings be upon him!
As for the hadith of Muʿawiyah:
Al-Tabarani narrated it in al-Awsat (7017) through the route of Muhammad ibn Ishaq, from al-Zuhri, from Ayyub ibn Bashir, who said: “I heard Muʿawiyah ibn Abi Sufyan,” attributed to the Prophet, peace and blessings be upon him. He cited it with the wording:
“Pour …”
Al-Haythami attributed it in Majmaʿ al-Zawaʾid (9/42) to al-Tabarani in al-Awsat and al-Kabir, then said:
“Its chain of transmission is good!”
I say: There are two observations concerning this:
First: the narration in al-Muʿjam al-Kabir (19, no. 792) is abridged and does not contain the hadith under the present heading.
Second: its chain of transmission includes Muhammad ibn Ishaq, who practised tadlis, and he narrated it using an ambiguous “from” formula.
It then became clear to me that its reports are inconsistent, and that the correct version is the hadith of ʿAʾishah.
Al-Tabarani narrated it in al-Awsat (5528) through the route of Muhammad ibn Ishaq, from al-Zuhri and Ayyub ibn Bashir al-Ansari, from ʿUrwah ibn al-Zubayr, from ʿAʾishah, from the Prophet, peace and blessings be upon him.