if a promise can reasonably be expected to induce reliance, and it in fact does, then the promissor can be estopped from denying the contract. that part's simple--this is clearly a promissory estoppel case and reliance is appropriate to the extent that justice requires.
reliance expenditures is what is important. the court will not put a value on the 'benefit' she received from the vacation. she did exactly what her uncle's promise intended to induce her to do.
the injustice is not relative to someone's idea of whether a vacation is a good thing. it's relative to her having done exactly what the promise called for, and having spent money in the process with the understanding that she would receive the benefit of the promise.
the injustice is in causing her to take an expensive vacation, which she might not have otherwise taken in order to be prudent with her money, and then denying to reimburse her for her expenses. i agree that it would be an injustice to give her more than her reliance expenses (the full 10k if she actually spent less), so she probably could only receive damages for the amount she can prove she spent.
the courts do rule like this (they don't care if it was a vacation, or a healthy lifestyle, or a new car, etc)... see Hammer v. Sidway and any promissory estoppel case.