She is listed twice in the 1911 census: living at home and at the work house.
Are you sure that it is a workhouse 
That's what I was thinking too Rosie, institutions can often be children's homes,schools,places for teenage girls to train for future work,or even hospitals.
I could then visualise Rose being included both at home and away,her parents not being sure in advance where she is going to be on census night.