Thus doing, she opens the epistemic negotiation
I think you describe the action very effectively - as an other-initiated repair with lots of very interesting non-vocal details - I'm not sure the notion of epistemic negotiation is helping though. I understand the relevance that the term invokes - and perhaps it would be useful in a broader discussion of this explicitly knowledge-centered activity of doing homework. However, using it in the analysis makes it sound to me as though they are managing the question of who knows the correct answer in the abstract. This kind of effaces the homework context - that this is a child 'testing' answers with a parent before committing them to paper for a test. There's questions of knowledge here - but I think your detailed description does more to explain how they're configured than this more generic term.