I know this may sound like the opposite of what you are attempting to do, but you would be much better off just admitting the truth to them instead of trying to live in a lie. They would definitely find out anyway; there isn't a very good way to hide such a major detail from them.
Believe it or now, a similar thing happened to me when I attempted to cut my own bangs at 7 years old. They came out incredibly uneven and odd-looking. I was in tears and was absolutely terrified to admit the truth to my mom and dad. My parents were angry at first, but eventually they calmed down and helped me fix the damage; now my bangs grew out and its like it never even happened.
As I mentioned before, its not like you can hide it from them. Just admit the truth and apologize, everything will be alright. Just remember, its hair. It can grow back in a few months/years (depending how much is cut off).
I hope this helps and that you and your family can get this sorted out :>
