There are a few problems with your code. Below is a minimal plugin example which should help you out. You do not want to try to relaunch your plugin (create a new instance of your plugin class). Instead, you should add a `parent` parameter to your map tool class constructor and pass in the plugin dialog when you instantiate the map tool class. This will allow you to access the dialog and it's widgets from inside the map tool class and simply show it on the right mouse click using `self.parent.show()`.

I have added some comments to the code below which is based on the minimal plugin example from Martin Dobias [here][1].

It is a simple, working example with all classes and methods within the `__init__.py` file and this example shows how I prefer to structure my plugins. I have also included the `metadata.txt` file so that you you can save both these files in a folder and copy to your plugins directory, then activate in plugin manager to test.

<!-- language: pyqgis -->

    from qgis.gui import QgsMapTool
    from qgis.core import Qgis
    
    from PyQt5.QtCore import Qt
    from PyQt5.QtWidgets import QAction, QDialog, QLabel, QPushButton, QVBoxLayout
    
    def classFactory(iface):
        return MapToolPlugin(iface)
    
    # Main Plugin class
    class MapToolPlugin:
        def __init__(self, iface):
            self.iface = iface
            self.canvas = self.iface.mapCanvas()
            self.dlg = MapToolPluginDialog()
            # pass in plugin dialog as parent (1st argument) to map tool constructor
            self.map_tool = ExampleMapTool(self.dlg, self.iface, self.canvas)
    
        def initGui(self):
            self.action = QAction('Go!', self.iface.mainWindow())
            self.action.triggered.connect(self.run)
            self.iface.addToolBarIcon(self.action)
            # connect dialog button signals to slot methods here (in initGui() method)
            self.dlg.ok_btn.clicked.connect(self.set_map_tool)
    
        def unload(self):
            self.iface.removeToolBarIcon(self.action)
            del self.action
    
        def run(self):
            self.dlg.lbl.setText('')
            self.dlg.show()
            
        def set_map_tool(self):
            self.canvas.setMapTool(self.map_tool)
            self.dlg.hide()
    
            
    class MapToolPluginDialog(QDialog):
        def __init__(self):
            QDialog.__init__(self)
            self.setGeometry(200, 200, 600, 250)
            self.lbl = QLabel('Get clicked coordinates', self)
            self.ok_btn = QPushButton('Set Map Tool', self)
            self.layout = QVBoxLayout(self)
            self.layout.addWidget(self.lbl)
            self.layout.addWidget(self.ok_btn)
        
    # Map tool class; takes parent & iface parameters in constructor
    class ExampleMapTool(QgsMapTool):
        def __init__(self, parent, iface, canvas):
            self.parent = parent
            self.iface = iface
            self.canvas = canvas
            QgsMapTool.__init__(self, self.canvas)
            
        def canvasReleaseEvent(self, event):
            click_point = event.mapPoint()
            posx = click_point.x()
            posy = click_point.y()
            if event.button() == Qt.RightButton:
                # access self.parent object
                self.parent.lbl.setText(f'Click Position: {posx}, {posy}')
                # access self.iface object
                self.iface.actionPan().trigger()
                # call show() on parent object (the plugin dialog)
                self.parent.show()
            elif event.button() == Qt.LeftButton:
                self.iface.messageBar().pushMessage(f'Click Position: {posx}, {posy}',
                                                    Qgis.Info, 5)


Metadata file:

    [general]
    name=MapToolPlugin
    description=Map Tool plugin
    about=Trivial example of a plugin with a map tool
    version=1.0
    qgisMinimumVersion=3.0
    author=Ben Wirf
    [email protected]
    repository=URL to the code repository


Short screencast showing result:

[![enter image description here][2]][2]


  [1]: https://github.com/wonder-sk/qgis-minimal-plugin
  [2]: https://i.sstatic.net/kZJTk.gif