Method chaining + inheritance don't play well together?

Is a Button really a Label? You seem to be violating the Liskov substitution principle. Perhaps you should consider the Decorator pattern to add behaviors to Widgets.

If you insist on the structure as is, you can solve your problem like so:

struct Widget {
    Widget& move(Point newPos) { pos = newPos; return *this; }
    virtual ~Widget();  // defined out-of-line to guarantee vtable
};

struct Label : Widget {
    Label& setText(string const& newText) { text = newText; return *this; }
    virtual Label& setAngle(double newAngle) { angle = newAngle; return *this; }
};

struct Button : Label {
    virtual Label& setAngle(double newAngle) {
        backgroundImage.setAngle(newAngle);
        Label::setAngle(newAngle);
        return *this;
    }
};

int main() {
    Button btn;

    // Make calls in order from most-specific to least-specific classes
    btn.setText("Hey").move(Point(0,0));

    // If you want polymorphic behavior, use virtual functions.
    // Anything that is allowed to be overridden in subclasses should
    // be virtual.
    btn.setText("Boo").setAngle(.5); 
}

I think (I haven't tested it) this will do it using templates:

template<class T> struct TWidget {
    T& move(Point newPos) { pos = newPos; return (T&)*this; }
};

template<class T> struct TLabel : TWidget<T> { ... }

struct Label : TLabel<Label> { ... }

struct Button : TLabel<Button> { ... }

Notes:

• Any/every base class needs to be a template, with a separate non-template leaf class at the top (contrast the LabelT and Label classes).
• The cast could be a dynamic_cast if you like.
• Instead of casting the "return *this", the base class could contain a T& as a data member (the derived class would pass this to the base class' constructor), which would be an extra data member, but which avoids a cast and I think may permit composition instead of or as well as inheritance.

This compiles on gcc 4.3.2 and is sort of a mixin pattern.

#include <string>

using namespace std;

struct Point {
    Point() : x(0), y(0) {}
    Point(int x, int y) : x(x), y(y) {}

    int x, y;
};

template <typename T>
struct Widget {
    T& move(Point newPos) {
        pos = newPos;
        return *reinterpret_cast<T *> (this);
    }

    Point pos;
};

template <typename T>
struct Label : Widget<Label<T> > {
    T& setText(string const& newText) {
        text = newText;
        return *reinterpret_cast<T *> (this);
    }
    T& setAngle(double newAngle) {
        angle = newAngle;
        return *reinterpret_cast<T *> (this);
    }

    string text;
    double angle;
};

struct Button : Label<Button> {
    Button& setAngle(double newAngle) {
        backgroundImage.setAngle(newAngle);
        Label<Button>::setAngle(newAngle);
        return *this;
    }

    Label<Button> backgroundImage;
};

int main() {
    Button btn;

    // oops: Widget::setText doesn't exist
    btn.move(Point(0,0)).setText("Hey");

    // oops: calling Label::setAngle rather than Button::setAngle
    btn.setText("Boo").setAngle(0.0); 
}

Well, you know it's a Button so you should be able to cast the returned Widget& as a Button& and keep going. It does look a bit ugly though.

Another rather annoying option is to create a wrapper in your Button class for the Widget::move function (and friends). Probably not worth the effort to wrap everything if you have more than a handful of functions though.