I don't mean to make you feel worse, but since this happened at your house, it really makes it more your responsibility to keep your beloved N7 safe from the mischievous hands of the kiddies. Had it happened at your aunt's house, it still would have been your responsibility, but maybe your aunt would have had a guiltier conscience and offered to help out. If they were my kids, I probably would have offered to pay for half, figuring you should have kept it hidden away from kids, as we all know that kids have a tendency to do these things. Then I would have made my kids do extra chores to make up for the cost and learn a lesson.
Anyway, since your aunt won't buy a new one for you, compromise a little and ask her for a short term loan. Tell her you understand it was your responsibility to keep the N7 away from her kids who shouldn't have touched it without your permission. But since they did touch it without your permission and then they broke it, ask her if she'd be willing to at least help out in this way.
How will you pay it back? I don't know anything about your lifestyle, but obviously either try to save a few dollars or try to make some extra money through overtime or offering to clean the gutters of your aunt's house or something like that. Forgo some things that you take for granted that cost money, but that you don't really think about. Do you go to Starbucks or the movies once in a while? Buy a soda for $2 at the 7-11 instead of drinking water? Cut down on these things, and within a couple months you'll have the money.
In the meantime, go to your aunt's house and "accidentally" break $200 worth of her china.
Sent from my fully functioning Nexus 7