I'm sure that with how few of them are left, it would only make sense for most of them to bring their babies with them everywhere, especially considering the way the Burnow Island facilities are.
Continuing in the story of Temre's burn recovery; her relationship with Quanin was already starting to bloom before she was wounded, but it flourished while she was recovering. Even when most of it was spent doped up on painkillers.
Temre's mother's name is Ny'ena. She's a field medic, and obviously was a big head in Temre's recovery.