snorkle,
as a kid who had piano lessons, didn't practise and never really got into it, and singing lessons, but was really into it because there was some extraneous motivation (singing groups, concerts etc), I would really second those who have said get her playing with others in some way to motivate her. Could she play with her brother, maybe some fun jazz stuff? (ok, maybe the viola not so suited to that). As she is only 11, it might be worth switching to a more versatile instrument where jazz etc might be an option.
I remember only too well how as a kid one wants to learn in the abstract, and enjoys the actual lessons, but the practice seems so divorced from anything that will bring you closer to the music and just becomes another boring homeworky type thing, of which there are millions. Added to her character of being a bit dreamy, (which I was) I can see how it's hard for her to get into it.. Singing I got really into because we sang as a family, and was also in groups and concerts etc, so there was something outside the boring old practice not leading anywhere..
best of luck, sounds like you're finding a solution!