I would say go and stay there anyway. For a young person who has already graduated or at least finished high school, one year out to reflect seriously on how they want to spend the rest of their life is not a long time. If, after one year, you decide that monastic life is not for you, at least you know what it entails, learnt something about meditation and the Dhamma, and gained some useful skills for lay life.
If you do find it is the right choice for you, by then your parents may have come around to accepting your choice. They may come out to visit you, and be happy to give their permission, or even participate by offering your monk's requisites, etc.
If they still don't agree, I guess there's still the "threaten to burn down the monastery" option