M.P.
What did her doctor suggest? Perhaps she'd cooperate if she's mildly sedated with an antianxiety medication. Perhaps a child therapist could help her.
I suggest continuing to get her co operation for 8 hours is likely reinforcing her need to not cooperate. That much time becomes a power struggle. No one wins. Threatening to leave her makes the situation worse by adding to her feelings of having no power and creates fear. You won't leave her. Making threats you cannot follow through on compromises your relationship. She will not believe you when you make other statements. She loses trust in what you say.
I suggest you back off, stop pushing her, allow her to save face. At this point, she's entrenched in no.
Have you and the LSP sympathized with her, explained why this is important and genuinely let her decide?