There is std::enable_shared_from_this just for this purpose. You inherit from it and you can call .shared_from_this() from inside the class. Also, you are creating circular dependencies here that can lead to resource leaks. That can be resolved with the use of std::weak_ptr. So your code might look like this (assuming children rely on existence of parent and not the other way around):

class A;
class B;

class A
    : public std::enable_shared_from_this<A>
{
public:
    void addChild(std::shared_ptr<B> child)
    {
        children.push_back(child);

        // like this
        child->setParent(shared_from_this());  // ok
        //               ^^^^^^^^^^^^^^^^^^
    }

private:     
    // note weak_ptr   
    std::list<std::weak_ptr<B>> children;
    //             ^^^^^^^^
};

class B
{
public:
    void setParent(std::shared_ptr<A> parent)
    {
        this->parent = parent;
    }

private:
    std::shared_ptr<A> parent;
};

Note however, that calling .shared_from_this() requires that this is owned by std::shared_ptr at the point of call. This means that you cannot create such object on stack anymore, and generally cannot call .shared_from_this() from within a constructor or destructor.