Did anyone else feel betrayed by the kid's choice of living with the dad and new wife, who was a mistress? And the email she sent with the photo as the happy family? Oh, I felt so hurt! No one else? And, honest, I don't know why I felt so hurt, it ridiculous, I know... Maybe too much feeling invested?

nope, youre not alone. I feel so betrayed and I ranted on SNS HAHAHA.
okay. yeah. I wouldnt do that to my mother, ever! 
Hahahahaa! It's nice to know that I'm not alone.... Gosh this kid... I was talking to  @khjfan01 about it and she was venting.... We talked and we still couldn't figure why it has to be part of the story line.... I hope Hye rim is happier than them... LOL
Oh, I didn't see that before, but I made a comment about that yesterday when I watched the episode, I felt so betrayed, I cried so much as if I was the mother, really, if my father abandoned me and my mother for a mistress I wouldn't even talk to him to begin with, but okay, there are different people in the world, but I just can't accept the fact she chose her father AND THE FUCKING MISTRESS instead of her mother who took care of her and dedicated her life to that ungrateful child, I'm so pissed, I wish she would regret it to the day she dies, she won't though, it's a drama and everybody will be okay with that on it...
Girl, welcome to the club!!!! Do you have any idea why would they include it in the story line? I'm looking for answers.... Maybe dramabeans knows...
That's a very good question, I don't understand it, really, very unnecessary, but I guess it's their way of getting rid of her daughter to help the romance, which makes no sense anyway, they could have just made her a divorcee without children if they were going to get rid of her daughter that way anyway.

Edit: Okay, that would make it look too much like One More Happy Ending, but... 
Ungrateful child, I wouldn't give her allowance. "Ask your father for money you traitor".
I think they included that story line so that despite the fact that mothers are overprotective of their children they are able to let them go if that makes the kid happy and if it's good for him/her, that's what I thought.
I know right! and she can't be so oblivious that she doesn't know how hard it was for her mother and how hard her mother is trying to support her studying overseas!!!!
She's a kid... She wants to spend time with her father, who seems like he isn't a bad person, he just made bad choices in the past...and the email was to assure her mother that she was all right. I understand how the mother feels, but at the same time as a mother she can't completely disregard how her daughter feels.

i do understand why you wanted to rant though... Those scenes were heartbreaking.

Also, I think they added it to show how self sacrificing her character is... The daughter and the ex-husband can be used as a plot point later if they want
Thank you @nicenoona for being the most rational person ever :)