It is very common for anorexic girls and boys to not want to eat with other people. This can include immediate family, extended family, friends or in public places.
In the early phases of recovery it will take every ounce of energy and determination for your child to begin eating more. I'm sure you have heard the phrase "pick your battles" in other parenting contexts. This phrase fits well in the context of eating disorders also.
Your first and foremost goal is to get your daughter to eat one more bite than desired at any given snack or meal. This will cause great anxiety for her and requiring her to eat with people she isn't comfortable with may be too much for her.
We have to remember recovery is a process. You don't want anything to distract you from the goal of re-feeding. The reality is if she is at a party where pizza is served she won't eat. So it is in her best interest to bring her home to eat.
As she continues to gain weight you will challenge her more to risk eating in places where she is less comfortable. This is an important part of her recovery.