What is the liability of a volunteer/friend for damages to furniture during a move?

If this was not a professional moving company then she has no recourse. That is the cost of moving, things get broken. But without any written contract, or proof of intent to vandalize I don't believe she has any case. I am sorry for your other daughter....and if I were you I would not offer to pay for the repair of the items for a daughter with an attitude like that. She can suffer the consequences of her actions (i.e. not supervising the move or protecting her furniture).