Yes, they could. You're right about that. But I think it's probable that given what little we know about the family, they will try to work this out. But it will never be the same. I just don't necessarily see the wholesale rejection and almost predetermined misery for Kara. Yes, her life will never be the same. And yes, her life could end up as many have written here it will. But I don't think it has to be that way. The choices that Kara makes from now on will help determine the path her future will take. She's still young and could have a bright future. But she has a tough road to hoe for certain.
Her choices may well be up to her alone from now on. Who's going to care enough to ground her or stop her from seeing a bad guy? If she doesn't cooperate until she's 18, she could end up being estranged from her family.