C++ :: Composition And Member Access Inside Composed Structure

I have a question regarding composition and accessing members "deep" inside the composed structure. For example;

class A {
private:
int m_myInt;
public:
int myInt() const {return this->m_myInt;};
void myInt(int newInt) {this->m_myInt = newInt;};

[Code] ....

Now, from somwhere I have access to an object of type B where I want to update the A::m_myInt. How would you do this without "breaking" the whole purpose of private/public members?

B myB;
myB.m_a.myInt(3); // Not allowed, and not desireable

I thought about implementing access through functons kind of like;

A & B::a() {return this->m_a;};
myB.a().myInt(3);

but I'm worried that this exposes my B::m_a-object too much. This would allow

myB.a() = A();
, right?

The following is a more desireable way of acces, but doesn't work for updating;

A const & B::a() {return this->m_a;};
myB.a().myInt(3); //Disallowed? myInt(int) is non-const.

What about this? Is this a good way of doing it?

class A {
private:
int m_myInt;
public:
int myInt() const {return this->m_myInt;};

[Code] ....

I guess it works? It would lead to a lot of data shuffling in case of larger sub-components.I would really like to do the following without exposing my components so much:

B myB;
myB.a().myInt(3);

Can it be done?