Flutter. How to correctly update state of nested widgets?

Question

I'm new in flutter and I'm trying to implement something like radio group with custom buttons in Android. For this I created StatefulWidget, which hold list of selectable buttons. For every button I was set press listener where I do something like this:

  setState(() {
      buttons.forEach((button) => button.isSelected = false);
      buttons[selectedButtonIndex].isSelected = true;
    });

And then my CustomButtonWidget changes color depending on the parameter isSelected .

All this works well. However, I have an additional requirement. I need my RadioGroupWidget to return the selected button type. For this I created a callback :

 final ValueChanged<ButtonType> onChanged;

And now my button press listener looking like this:

onTap: () {
      setState(() {
          buttons.forEach((button) => button.isSelected = false);
          buttons[selectedButtonIndex].isSelected = true;
        });
      onChanged(buttons[selectedButtonIndex].type);
}

Next I get this type of button in my other widget which is using RadioGroupWidget:

CustomRadioGroup(
   onChanged: (value) {
       setState(() {
          buttonType= value;
        });
    }),
) 

As you can see I call again setState. This is what leads to the problem. But I need to do this, because I need to update the state of another widget (for example let's call it InfoWidget) depending on the selected button.

After all these manipulations, the state of the InfoWidget is updated correctly, but the state of the selected button in the RadioGroupWidget does not change. I tried to debug this and I see that at first the parameter isSelected is set to true for the desired button, but after the state of the button I selected is not updated, because its parameter isSelected becomes false. And I don't understand why this is happening.

Please help, I am completely confused.