It sounds like your dd has three diagnoses that the school may respond to with at least a 504. The ADHD and anxiety Dxs both have implications for organization and social skills, and would warrant a 504 in most settings.
In a larger group of children, she may be having difficulty attending to and reading all of the social cues (factors associated with both ADHD and anxiety), which can be very frustrating. In a 1:1 or small group, there isn't as much data flying around that she has to capture, interpret, and organize, and then manage impulsivity to execute the appropriate response. I imagine she finds it quite exhausting to put all of this together in a larger group of children.
Adults naturally scaffold and structure for children, so it's much easier to interact socially with adults. It's possible that when she knows you are present, she unconsciously expects you to do more scaffolding for her.
What might be helpful for her is to talk through and role-play some skills for reading others emotions, and dealing with common interpersonal conflicts that come up between kids. Practice them in a nonlive setting first, then in sheltered live settings (such as with a sibling or a one-on-one playdate), with coaching and cueing in real-time, and then a (private) balanced review of how the skills were executed or could be improved, and how the situation turned out, after the incident. If this is with a sibling or very understanding peer, (you have to be pretty careful here) it can be helpful to get feedback from the other child as well (you'll have to coach the other child before you start doing this, as well as through the live process, so they are not too brutally honest).
Once she becomes comfortable with the process to this point, you can start asking her to tell you how she was able to apply it independently, and reinforcing her when you observe her applying any part of it independently. I wouldn't work on more than one skill at a time.
An excellent resource for this is Ellen McGinnis's "Skillstreaming the Elementary School Child" (based on the research of the late Dr. Arnold Goldstein). It's designed for small group use, and is pretty much the standard for structured social skills groups in schools.
