>>2's right. Let things flow naturally. For now, just comfort your mom in any way possible, and tell her that it's not her fault. Although I really don't get why your sister would run away and act so aggressive towards your mother. I mean, sure your mother really should've just left her alone to adjust, but to send her home
crying?
Dammit though, I hate it when I start acting like a devil's advocate, because now I'm wondering: Are sure your mom, dad, or even yourself never did ANYTHING wrong to her that would cause her to run away? If not, then she honestly sounds like one of those people who read too many fairy tales about true love and thinks that they're achievable :/