According to Jewish law, she has been an adult for a year already. I’m not saying that you should treat her the same way you would treat a twenty-year-old, but just remember that even though she will always be your child, she is already well past the midpoint of her childhood and is steadily gaining in her ability to make decisions on her own and exercise her own judgment. I have a thirteen-year-old brother, and sometimes I have to consciously remind myself that he’s not a little kid anymore. I know it can be hard to acknowledge that children outgrow childhood, because he’ll always be “my little brother”, but at the same time he amazes me with his intelligence and maturity.
I can’t imagine what could possibly be in Yated that would be inappropriate for a thirteen-year-old. Nevertheless, if you are uncomfortable with her reading it, you have the right to take away that privilege. Just do her the courtesy of explaining in a rational way why you do not want her to read it. If she can understand what exactly is so objectionable about the content, she will be less likely to seek it out elsewhere, away from your watchful eye.