How old is your DD?
My DD is an only and we didn't do any formal lessons until she was about 8. Although I should say we were in a HS co-op for a couple of yrs 1 day a week where she did have a classroom-like situation. (But, in retrospect, I wish we had not done the co-op.)
My DD is pretty imaginative and engaged herself in some fantasy play (dolls, legos, cars, etc.) and our HSing was very relaxed for those earlier years. Even now, when she is 9yo she can only handle minimal sit-down type of work b/c she is kinesthetic.
I don't know much about your situation, but it could be that your DD needs some more outlets for her imaginative play or a different style of HSing. I'd be curious to know what her enrichment program looks like. Perhaps that contributes to the scenario you describe. It would stand to reason that she would come to expect her school at home to look like her day at the enrichment school.