I don't see why Luna would leave in any case. She's already an independent person for all intents and purposes, with the kind of history she had. Even if her relationship with the mother had immediately become splendid, Luna considers that town and house her home now, so she obviously wouldn't go anywhere. She's not going to leave her own established life behind. The mother's situation seems to be different because she hasn't got an established life, by the looks of it. She's basically a vagrant, to put it bluntly. Luna would be worse off following her anyway. If Elsa was smart, she would start working in that very town and make a life for herself there. That way she could meet Luna whenever it's convenient, but they would still live their own lives, like two adults would.