Answer: The book is NurtureShock, by Po Bronson and Ashley Merryman. It'll help on your other counts, too.
Also, as you'll find out soon, the helicopter- and the kid-run-wild problems are two separate things.
Helicoptering is when you prevent your child's every fall, literally and figuratively. It's when you catch them mid-stumble even when they're headed for nothing more serious than a brush with the nearby floor. It's when you run to them panic-stricken every time they cry, and keep them off anything that might skin knees or break arms. It's when you fight their battles for them, and when you browbeat them onto the path to excellence at whatever key excellence-indicator you choose for them, be it reading or playing a musical instrument or sport or speaking a foreign language.
A helicopter parent will tell you it's about protecting the kid, but it's really about protecting the parent from the harrowing business of letting go.
The "anti-helicopter parent" presumably also wants a kid to be successful, of course - but allows a little more room for error. Kids need to be taught the age-appropriate basics of whatever new thing they take on - walking, bikes, crossing streets, etc. - and then, when both you and kid are confident of kid's ability, you start letting go in age-appropriate increments.
What are those? Well, depends. Using your judgment, your kid's abilities, and a general sense of child-development milestones will get you in the ballpark.
The run-wild thing is about civilizing your kid - when hovering is necessary and good. In a restaurant, for example, you watch your kids closely, correct them gently and firmly, and remove them when they won't stop screaming/throwing food/etc. . . . a full list of "don'ts" is on view at most family restaurants.
Civilizing means you never, ever hand your kid a cookie when s/he says, "Give me a cookie," even when refusing means a tantrum. Ever hear kids talk to their parents like that? It curdles air. It's also completely preventable by setting the bar as soon as they're old enough to say "peash" and "shankoo." Again, that's not helicoptering, that's being a parent.
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