I think that you handled the situation well- so would not beat yourself up about it.
Another thought for you- while this is rec, you have a team of 7 other girls who are there to play and have fun- and this girl's behavior is detracting from their experience. Even in 10U- I think part of the experience involves girls understanding "team rules" and "team behavior" and being able to work within a framework that is age appropriate for them. At the very least, maybe it would be helpful to talk with her at a time when the situation is more remote- and go through the events to find out what prompted that melt down- and how something like that could be avoided in the future.
Another thought for you- while this is rec, you have a team of 7 other girls who are there to play and have fun- and this girl's behavior is detracting from their experience. Even in 10U- I think part of the experience involves girls understanding "team rules" and "team behavior" and being able to work within a framework that is age appropriate for them. At the very least, maybe it would be helpful to talk with her at a time when the situation is more remote- and go through the events to find out what prompted that melt down- and how something like that could be avoided in the future.