she finds out like in a total gotcha scene. Like, there is this new ship, they go in to investigate and bam, suddenly parents. Or she goes there alone and they tell her that they are here to talk to Mon-El of Daxam and bam, suddenly reveal that they are the parents.

Like I wouldn't be surprised if the queen tells Kara, not Mon-El himself. Maybe it goes that far that that "toast" scene is where she finds out. Kara's gonna be so pissed.