Linkle uncannily looks like Ilia and Link. Is she their offspring?
The Zelda IP exists across multiple continuities, a fact that Hyrule Warriors (and/or Legends) exploits in its backstory (emphasis mine)
Long ago, Ganondorf was defeated and his soul splintered into four fragments. Three of them were were sealed in different moments in time, while the fourth was trapped by the Master Sword. But Ganondorf plots his resurrection through Cia, a sorceress who protects the balance of the Triforce while maintaining neutrality. Cia becomes fascinated with the spirit of the Hero of Legend, with her amorous feelings for the hero providing Ganondorf an opportunity to purge her inner light. As a result, Cia becomes consumed in her desires, opening the Gate of Souls, a portal to different time-space realities of Hyrule, to amass an army of monsters. Seeking to unite the Triforce and conquer Hyrule, she uses her subordinates Volga and Wizzro to wage war against Princess Zelda and the Hyrulean army.
Ilia comes from the Twilight Princess continuity, but Linkle's village clearly does not exist there, since Linkle has to travel to that era as part of the game. As such, it is not possible that she could be Linkle's mother (at least not the Twilight Princess version of her). Since we know nothing of Linkle's parents, it's still possible that her reality has some other version of Ilia.