Depending on the number of shots that the photographer go and her editing skills, she might be able to cobble together one or two of the entire family looking good. She would take one kids good face shot and put it on another image where the kid had eyes closed, etc.
It's perhaps worth asking for an additional small fee.
As a photographer, I don't think I would EVER give a client 300 shots to choose 15! Ouch...BUT... think what she is asking for is reasonable.