C# WPF 任意の座標にマウスポインタを移動してクリックイベントを発生させる

<Window x:Class="MouseCommander.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        Title="MainWindow" Height="90" Width="250">
    <Window.Resources>
        <ResourceDictionary>
            <Style TargetType="Button">
                <Setter Property="Margin" Value="10 0 0 0"></Setter>
                <Setter Property="Width" Value="100"></Setter>
                <Setter Property="Height" Value="30"></Setter>
            </Style>
        </ResourceDictionary>
    </Window.Resources>
    <Grid>
        <StackPanel Orientation="Horizontal" 
                    Margin="10"
                    Height="30" HorizontalAlignment="Right" VerticalAlignment="Bottom">
            <Button Name="startButton" Click="StartButton_Click" >開始</Button>
            <Button Name="stopButton" Click="StopButton_Click">終了</Button>
        </StackPanel>
    </Grid>
</Window>

using System;
using System.Collections.Generic;
using System.Linq;
using System.Runtime.InteropServices;
using System.Text;
using System.Threading.Tasks;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Imaging;
using System.Windows.Navigation;
using System.Windows.Shapes;

namespace MouseCommander
{
    /// <summary>
    /// MainWindow.xaml の相互作用ロジック
    /// </summary>
    public partial class MainWindow : Window
    {
        [DllImport("USER32.dll", CallingConvention = CallingConvention.StdCall)]
        private static extern void SetCursorPos(int X, int Y);

        [DllImport("USER32.dll", CallingConvention = CallingConvention.StdCall)]
        private static extern void mouse_event(int dwFlags, int dx, int dy, int cButtons, int dwExtraInfo);

        private const int MOUSEEVENTF_LEFTDOWN = 0x2;
        private const int MOUSEEVENTF_LEFTUP = 0x4;

        public MainWindow()
        {
            InitializeComponent();
        }

        private void StartButton_Click(object sender, RoutedEventArgs e)
        {
            var stopButtonPosition = stopButton.PointToScreen(new Point(0, 0));
            SetCursorPos((int)stopButtonPosition.X + 1, (int)stopButtonPosition.Y + 1);
            mouse_event(MOUSEEVENTF_LEFTDOWN, 0, 0, 0, 0);
            mouse_event(MOUSEEVENTF_LEFTUP, 0, 0, 0, 0);      
        }

        private void StopButton_Click(object sender, RoutedEventArgs e)
        {
            MessageBox.Show("終了");
        }
    }
}