When you apply for insurance, you answer a set of standard questions such as where is the car kept overnight and what is the main purpose of driving the car (e.g. commuting). What you're saying here suggests that for 2.5 weeks, this will change. I can't see this being an issue, as you could take the car on holiday for that length of time and that would not be an issue. I think what has to be watched out for here is any suggestion that your parents have insured a car but it's primarily for your use. As long as that is not the case, I can't see an issue.
Obviously if something happens to the car on your watch, and a claim is made, that will affect any existing no claims bonus (though your parents may pay extra to protect this). Any claim is likely to increase next years quote.
Other than that, I can't see a problem here.