Just something I am wondering after seeing them address the public in North Qeynos. They seem to have animosity between them and why is Kyle in that form?
It's been too long since I've done those quests to directly answer your quests. Kyle Bayle was first introduced during the Claymore timeline in Kingdom of Sky, though with a rather minor role. The City of Qeynos timeline gives much more information about their relationship. The shortest version of it is that Kyle wasn't in the direct line for the throne, and he "died" many many years ago.
It's part of the City of Qeynos questline where Antonia's estranged brother claims to rightfully have claim to the throne. Go speak with Murrar Shar in the Harbor to get started on the questline.