When one of the trees in my garden was blown over during a gale, it damaged my rear hedges, lay across a bridle-path and took out a few fence panels of my neighbour's property the other side of the bridle-path, and did extensive damage to the 6" gauge railway that runs around his garden. Fortunately it missed the roof of his swimming pool, had it fallen a bit further the other way it would have landed in his tennis court.
On consultation with my Insurance Company I was told that unlike car insurance, building insurers do not try and apportion blame. My Insurance Company undertook to pay for damage to my property, but that my neighbours Insurance Company would have to pay for damage to his property. I had originally, as had he, wrongly assumed as it was my tree my Insurance Company would accept liability and pay for all repairs. It wasn't pleasant telling him that, but his Insurance Company confirmed it.
This is why the OP's daughter is having difficulty getting buildings insurance, they are reluctant to take liability for damage to her property from a neighbour's large and very close tree. They would not be as reluctant to insure, if they knew any damage to the OP's daughter's property would be the liability of her neighbour, or their insurance company.
So, most certainly the OP's daughter would be liable for any damage to her property in the event the tree is the culprit! I would suggest that the OP's daughter consults an Insurance Broker, rather than individual Insurance Companies. The Broker will have wider knowledge of Insurance Companies who are prepared to accept higher risk, but that is likely to come with a higher insurance premium than if the possibility did not exist. However that may well outweigh the cost of any repairs.
I would also be concerned about damage to the property's foundations caused by root spread. Root spread is normally about the same distance as the tree's canopy spread. The neighbour would certainly bear liability for any damage caused by root spread, so that may be another discussion point with the neighbour.