Just be glad that you or your family has the means to pay for braces. I wish I could have had proper dental care when I was young. I'm sure they are no fun, but you will have beautiful teeth when its all said and done.
I dont think that you would need to bend the edge over to make it secure. I would look at how and with what the tin was secured to the top of the coop. My guess is that either the wrong type of fastener was used, or not enough of them. Post a picture, I'm sure there is an easy fix.
Matt