_Taame Haminhagim_ 579 says _Sh'ne Luchos Hab'ris_ [circa 1600] indicates one should memorialize _Ester_'s meal at the meal of the second day of _Pesach_, as that was the day _Haman_ was hanged. He doesn't say how to memorialize it, but I guess _Shoshanas Yaakov_ is one way to do it.

*Update:* Thanks to [Aba](/users/9163/aba), who found [the _Sh'lah_](http://www.hebrewbooks.org/pdfpager.aspx?req=14406&pgnum=381) (in the _hagaha_ on the linked-to page). Note that it doesn't use "oughta" language like the _Taame Haminhagim_: it says, rather, that some who are careful do so. And it adds (as the _Taame Haminhagim_ doesn't) that the purpose of this practice is to mention the praises of God [which makes the singing of _Shoshanas Yaakov_ seem to me to be a good implementation of this practice].