Focus CellEditTemplate on double click cell DataGridRow WPF

I have a datagrid and want to show hyperlink and normal text in cell at a time .I have defined celltemplate and celleditingtemplate for cells in the datagrid. I have set the selection mode to be a full row.

When i click on hyperlink after that cell editing is not enable unless i change focus from it. I want to edit cell after click on hyperlink. When i double click on cell then it should be edit.
Any suggestions ? Please see my code below

  <my:DataGrid Name="Grid"  HeadersVisibility="Column"    SelectionUnit="FullRow"
                                                    HorizontalAlignment="Stretch" VerticalAlignment="Stretch" ItemsSource="{Binding Notes,UpdateSourceTrigger=PropertyChanged}" Background="White"  AutoGenerateColumns="False"
                                                   BorderBrush="#FFB1B1B1" VerticalScrollBarVisibility="Auto" HorizontalScrollBarVisibility="Auto" 
                                                     HorizontalGridLinesBrush="LightGray" ScrollViewer.CanContentScroll="False" VerticalGridLinesBrush="LightGray" CanUserDeleteRows="False" CanUserResizeRows="True"  CanUserAddRows="False">
          
            <my:DataGrid.Columns>
                <my:DataGridTextColumn Binding="{Binding Path=TimestampString}" Header="Timestamp" IsReadOnly="True"/>
                <my:DataGridTemplateColumn Header="Notes"  Width="*">
                    <my:DataGridTemplateColumn.CellTemplate>
                        <DataTemplate>
                            <StackPanel  Width="Auto" Background="White"  >
                                <TextBlock    Name="tb"   Style="{DynamicResource TextBlockStyle}" TextWrapping="Wrap"   Helpers:NavigationService.Text="{Binding Notes}"  ContextMenu="{StaticResource TextBoxContextMenu}"></TextBlock>
                            </StackPanel>
                        </DataTemplate>
                    </my:DataGridTemplateColumn.CellTemplate>
                    <my:DataGridTemplateColumn.CellEditingTemplate>
                        <DataTemplate>

                            <TextBox AllowDrop="False"  AcceptsReturn="True" TextWrapping="Wrap" Name="Note" Text="{Binding Notes}">                              
                            </TextBox>
                            <DataTemplate.Triggers>
                                <Trigger SourceName="Note" Property="IsVisible" Value="True">
                                    <Setter TargetName="Note" Property="FocusManager.FocusedElement" Value="{Binding ElementName=Note}"/>
                                </Trigger>
                            </DataTemplate.Triggers>
                        </DataTemplate>
                    </my:DataGridTemplateColumn.CellEditingTemplate>
                </my:DataGridTemplateColumn>
            </my:DataGrid.Columns>


        </my:DataGrid>