My kids all asked me to join, but I restrict it to just that. I don’t want my name linked to anybody I don’t know well.
You’re being paranoid. If you friend them, you have a better way to keep tabs on your daughter. You can see what she’s posting on their walls, you can see pictures posted by friends, etc. By sending you a friend request they’re basically saying they trust you and are trustworthy themselves. They know what you can and can’t see. Go ahead and add them.