template<class T> class MyPointer
{ //This class differs from simple pointer by having someAdditionalData
private:
  T *pointer;
  int someAdditionalData;
public:
  inline MyPointer(void): pointer(NULL), someAdditionalData(0) {;} //Default constructor
  inline MyPointer(MyPointer<T> const &p): pointer(p.pointer), someAdditionalData(p.someAdditionalData) {;} //Copy constructor
  inline MyPointer(T *const p): pointer(p), someAdditionalData(0) {;} //Custom constructor
  inline MyPointer<T> *operator->(void) const {return pointer;} //Arrow operator
  inline MyPointer<T> &operator*(void) const {return *pointer;} //Dereference operator
  inline int &SomeAdditionalData(void) {return someAdditionalData;} //Really important method
};

I also have another class which this pointer points to:

struct ClassToPointTo
{
  int firstMember;
  int secondMember;
};

MyPointer<ClassToPointTo> GeneratePointer(void)
{
  //Some code here which calculates pointer and its someAdditionalData
}

...

MyPointer<ClassToPointTo const> const p( GeneratePointer() ); //I really like to write "const" where I can

The first problem is that MyPointer<ClassToPointTo> is not automatically converted into MyPointer<ClassToPointTo const> (I know why, but I don't know how to fix it), and the second, the main problem is following:

I need to convert pointer p from " ClassToPointTo const " type into one that will point to the firstMember of *p object *without losing someAdditionalData *. I have function GeneratePointer() which will make pointer having someAdditionalData , but I need to work only with pointers to firstMember s of the objects:

MyPointer<int const> const p( WhatINeedToWriteHere??? GeneratePointer() ??? );

I need fast and good-looking way of doing such conversion.

The first problem is that MyPointer<ClassToPointTo> is not automatically converted into MyPointer<ClassToPointTo const> (I know why, but I don't know how to fix it)

Maybe like this?

template <typename T>
class MyPointer;

template <typename T>
struct MyPointerConversion
{
    operator MyPointer<const T>() const
    {
        // ...
    }
};

template <typename T>
struct MyPointerConversion<const T>
{
};

template <typename T>
class MyPointer : public MyPointerConversion<T>
{
    // ...
};

A conversion constructor doesn't work because you would have to write

MyPointer(const MyPointer<typename remove_const<T>::type>& origin);

which might have the same signature as the copy constructor ( remove_const is a metafunction that removes the const qualifier from a type).

Concerning your second problem: Can't it be solved by using a conversion operator (or better a function, to avoid implicit conversions), too?

A conversion constructor doesn't work because you would have to write

MyPointer(const MyPointer<typename remove_const<T>::type>& origin);

which might have the same signature as the copy constructor ( remove_const is a metafunction that removes the const qualifier from a type).

sfinae helps

template <typename U>
MyPointer(const MyPointer<U>& origin, typename enable_if< is_same< T, const U > >::type* = 0);

A template constructor is never a copy constructor.
with meta functions is_same and enable_if, which can be found in tr1 or boost.

derivation could be used as well, T->const T would then involve intentional slicing

template<class T> class MyPointer : public MyPointer< const T >
{
...
// hide any functions from base or overload with using, depending on whether constness is supposed to be transitive or not
};

template <class T> class MyPointer< const T >
{
...
};

template<class T> class MyPointer
{
...
// eat any MyPointer and a corresponding pointer to member
    template <typename U, typename V>
    MyPointer(const MyPointer<U>& other, V U::* pm  )
        :  pointer( &( *other ).*pm ), someAdditionalData( other.SomeAdditionalData() )
    {}
...
};

MyPointer<ClassToPointTo const> const p( GeneratePointer(), &ClassToPointTo::firstMember );

template<class T> class MyPointer
{
...
// eat any MyPointer and a corresponding pointer to member
    template <typename U, typename V>
    MyPointer(const MyPointer<U>& other, V U::* pm  )
        :  pointer( &( *other ).*pm ), someAdditionalData( other.SomeAdditionalData() )
    {}
...
};

MyPointer<ClassToPointTo const> const p( GeneratePointer(), &ClassToPointTo::firstMember );

Last 2 weeks I trying to understand this but without any success.

&ClassToPointTo::firstMember
Such pointers are beyond my understanding.

I think this should be an ordinary memberfunction pointer:
http://www.newty.de/fpt/callback.html#member

It could be a pointer to member function if V is a function type, but that would be pointless with regards to the purpose of that class. I was thinking of a pointer to an ordinary non-function member.

I need to convert pointer p from " ClassToPointTo const " type into one that will point to the firstMember of *p object *without losing someAdditionalData *. I have function GeneratePointer() which will make pointer having someAdditionalData , but I need to work only with pointers to firstMember s of the objects:

MyPointer<int const> const p( WhatINeedToWriteHere??? GeneratePointer() ??? );

I need fast and good-looking way of doing such conversion.

I'm afraid that particular pig won't fly. At least not without a global map, which again is problematic and/or slow in multi-threaded environments.

If there were a "good" way (whether eays or not), I'm sure one of the smarter among the C++ community would already have found it, and integrated it into the boost::shared_ptr implementation. (As a way to get a shared_ptr from a raw-pointer, that shares ownership with other existing shared_ptrs.)

(ungetestet)