I was a counselor at Flip Fest a few years ago and most weeks I had little ones in my cabin. Some did better than others, but overall I think they all did really well. Some came with teammates and some just made friends with other girls in the cabin from other gyms. Homesickness was really not a huge problem, at least for my groups. Girls who stayed for
At Flip Fest there is a phone girls can use to call home whenever they need to during the day if they have a calling card which is different from some camps which don't allow calls home until the end of the week. This can be good for some, not so great for others.
A lot of times younger girls that come with their team have a team parent come along to be the cabin counselor. That way they are in the cabin with an adult who they are familiar with and who knows the individual child. So if your daughter comes with her team, maybe you or another team parent could travel along. Also, traveling with older teammates can help some of them. Two of the girls who had the biggest problem in my cabin had older teammates in another cabin and went to them with problems.
Since you are an RN, you could probably get a position at camp. In those positions, I think you can have your daughter stay in your cabin with you. She still gets to go to the gym, participate in all the activities, and make new friends. Even if she stays in her own cabin, you can visit her frequently, watch her in the gym, eat meals with her, so there is lots of interaction. I would definitely look into that if you are interested, when I was there they had some problems finding medical staff for some weeks.