I do hope Emily is seeing a good therapist at least once a week. It's going to take her a very long time to heal and she's going to need a great deal of support. Also group therapy with other teenages with similar problems might be helpful.
I tend to think that Emily first needs to establish not only feeling safe and trust among family members, she also needs to learn that she is an important member of the family and that she is loved and this takes a lot of time and patience.
Everyone in the family should spend quality time with her alone, doing something she might enjoy as well as she should attend a lot of family activities. So get the family together for Picnics, games, cook-outs, sit down dinners, bowling, movies, day trips etc. and ask her for help in getting things ready..."come Emily, help me set the table"..."help me load the car" etc..and always let her know what a big help she was. Then you might say, come Emily, lets wash our hands before we sit down...and even if she doesn't end up washing her hands, she sees the process as you are talking to her....
Next time you go to the hair dresser ask her to come with you to keep your appointment. Don't ask her to get her hair done....just let her watch everything around her while you get your hair cut etc....and then take her out for lunch and go window shopping with her....Play the game of "Oh, I love that...which one do you like..."
you might ask her to sleep over...Prepare a bubble bath...don't ask her to get in...but invite her to sit in the room with you while you are in the tub...mention how great it feels and then talk to her about what she's learning in school or something she might like talking about.
or have her join you in the room while you are brushing your teeth, or scrubbing your face or applying make up.
the point is the more she see's of grooming, and different styles of clothing, she might begin to want to follow up on it on herself.
You might also buy her some teen magazines which always covers grooming ideas, style of clothing and then a few days later ask her what she enjoyed about the magazines.
In terms of landing that job, you might sit her down to talk if she doesn't land one...ask her what she thinks the problem is, what she thinks what went wrong with the interviews and what she thinks she might change that will be helpful in landing a job. Listen to her answers, her feelings....then ask her if she's willing to listen to some suggestions. She might consider the help you can give with this...or not but it's a start in planting some seeds into thinking differently about it..
I don't think that her classmates poking fun of her is helpful at all...but nothing for this as that's what kids do. But when she talks about it ask her what she thinks she can do to change this from happening...listen and then make a suggestion that the best way she can put a stop to it is if she wants to, by grooming herself. And if she wants to go up that road, let her know you'll be happy to help her with it.
Depends on how far she wants to take it. She might not know where to start or have the money for these things she needs to get started with this.