Cook County public defender Amy Thompson filed the 19-page motion Friday seeking a new trial for William Balfour, 31, the Chicago Sun-Times reported.
Balfour was convicted in May of killing Hudson's mother, brother and 7-year-old nephew out of jealousy that his estranged wife -- Hudson's sister -- was dating another man.
Prosecutors called Hudson as the first witness in the April trial, in which she testified she never liked her former brother-in-law and she begged her sister, Julia, not to marry him.
"[Hudson's] testimony was irrelevant, and because of the fame of the witness, the prejudicial effect of the testimony on the jury far outweighed any probative value that it would have," the document said.
The defense is also requesting a new trial, in part, because prosecutors alerted them to "a potential alternate suspect" after a jury had already been selected, three days before opening statements, the filing said.
Balfour's lawyers also alleged assistant state's attorney James McKay made "improper and inflammatory" statements about the defendant, saying "Calling the defendant a 'dog' is an insult to dogs," the Sun-Times reported.
Judge Charles Burns scheduled a hearing to consider the new trial request for July 24. If he denies a new trial, he could sentence Balfour that day, the Chicago Tribune reported.