Not sure where the coordinates will come from, but let's assume it will be a dependency property on your custom button. You can then programmatically bind to that property from your menu. There will be a dependency property on your menu that the binding is set to update. You can then bind to that property from the textbox so that the canvas coordinates get updated. You can also update the visibility of the textbox using an IValueConverter that converts a bool (another dependency property linked between the button and menu) to a visibility value. Not sure I understood your question correctly, but hopefully those ideas will help you get a start.
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