Can you charge him £25 for the bother of you having to research his effing holiday plans for him?
You cannot let her go under these circs. Imagine if something happened and you didn't know where she was. Why not let him get himself there and then you'll get her there, i.e. by car or even by coach yourself? (Not ideal obviously but .. )
A friend of mine, when she was a bit older, maybe 9, went to stay with her dad in London (mum lived in Paris). The first night they went to the pub (as one does ) and then slept the night in his van as he wasn't able to drive home. Next day he went off to work (builder), leaving her 50 quid to 'amuse' herself with during the day. Like a 9-year-old would know how to spend 50 quid (well, this was in the seventies, prob now they'd be day-trading and buying iTunes!). That night, same story, somehow 'couldn't' get to his lodgings - obviously he didn't have any, despite swearing blind to the mum he did. They slept in the van.
Next day she phoned and said it's awful, and the mum had to arrange for her to get to Heathrow and fly back to Paris. Dundee isn't Paris (alas) but why take that risk.