Yes! I think she would love to share those kinds of experiences with her kids, particularly as they start getting older (no longer baby baby)... I think she'd want her kids to know there's a whole world out there to explore and make a name for themselves in, if they want to. She loves to travel, too, so... it's an inevitability that they would come along for some of the trips.

I'm sure at a certain point she takes them with her to Gridania and shows them where she grew up. She'd want to introduce her kids to her tribe, but sadly they all up and vanished post-Calamity... (': At this point I've basically decided that her dad is technically alive, but he and Arc have a pretty distant relationship, so I'm not sure if he ever meets his grandkids... but he might.