wpf DataGridTemplateColumn CellEditingTemplate - combobox's itemssource issue

Question

I have TabControl with two items.

    <Window x:Class="WpfApplication1.MainWindow"
            xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
            xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
            Title="MainWindow" Height="350" Width="525">
        <Grid>
            <TabControl>
                <TabItem Header="Tab1" Content="{Binding}" ContentTemplate="{StaticResource Tab1}"/>
                <TabItem Header="Tab2" ContentTemplate="{StaticResource Tab2}"/>
            </TabControl>
        </Grid>
    </Window>

There are DataGrid control in one tabItem of TabControl. DataTemplates of TabItems:

    <DataTemplate x:Key="Tab1">
        <DataGrid ItemsSource="{Binding Entities}" x:Name="dataGridEx">
            <DataGrid.Columns>
                <DataGridTextColumn Binding="{Binding Name}" Header="Name" Width="100"/>
                <DataGridTemplateColumn Header="Position" Width="150">
                    <DataGridTemplateColumn.CellTemplate>
                        <DataTemplate>
                            <TextBlock Text="{Binding Position}"/>
                        </DataTemplate>
                    </DataGridTemplateColumn.CellTemplate>
                    <DataGridTemplateColumn.CellEditingTemplate>
                        <DataTemplate>
                            <ComboBox SelectedItem="{Binding Position, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}" 
                                      ItemsSource="{Binding Path=DataContext.Positions, RelativeSource={RelativeSource FindAncestor, AncestorType={x:Type DataGrid}}}"/>
                        </DataTemplate>
                    </DataGridTemplateColumn.CellEditingTemplate>
                </DataGridTemplateColumn>
            </DataGrid.Columns>
        </DataGrid>
    </DataTemplate>

    <DataTemplate x:Key="Tab2">
        <Grid>
            <TextBox Text="Empty tab"></TextBox>
        </Grid>
    </DataTemplate>

DataContext of MainWindow:

public class MainWindowViewModel
{
    public ObservableCollection<Entity> Entities { get; set; }

    public List<string> Positions { get { return new List<string>() { "Manager", "Seller" }; } }

    public MainWindowViewModel()
    {
        Entities = new ObservableCollection<Entity>()
                       {
                           new Entity() {Name = "John", Position = "Manager"},
                           new Entity() {Name = "Mark", Position = "Seller"},
                           new Entity() {Name = "Alice"}
                       };
    }

}

The Entity class:

public class Entity : INotifyPropertyChanged
{
    private string _name;
    private string _position;

    public string Name
    {
        get { return _name; }
        set
        {
            _name = value;
            OnPropertyChanged("Name");
        }
    }
    public string Position
    {
        get { return _position; }
        set
        {
            _position = value;
            OnPropertyChanged("Position");
        }
    }

    #region INotifyPropertyChanged

    public event PropertyChangedEventHandler PropertyChanged;

    private void OnPropertyChanged(string property)
    {
        if (PropertyChanged != null)
            PropertyChanged(this, new PropertyChangedEventArgs(property));
    }

    #endregion
}

Application is running. I edit the Position column. Then I switch to the 2nd tab and then the 1st tab again. Position value of edited row is deleted.

If I write data directly to tabItems - it works okay

        <Grid>
            <TabControl>
                <TabItem Header="Tab1">...</TabItem> 
                <TabItem Header="Tab2">...</TabItem> 
            </TabControl>
        </Grid>

But I need to use DataTemplates for tabItems in my solution.

I have some idea.. Using style, not datatemplate inside editing mode

    <DataGridComboBoxColumn Header="Position" SelectedItemBinding="{Binding Position, UpdateSourceTrigger=PropertyChanged}">
            <DataGridComboBoxColumn.ElementStyle>
                    <Style TargetType="ComboBox">
                            <Setter Property="ItemsSource" Value="{Binding Path=DataContext.Position, ElementName=dataGridEx}" />
                    </Style>
            </DataGridComboBoxColumn.ElementStyle>
            <DataGridComboBoxColumn.EditingElementStyle>
                    <Style TargetType="ComboBox">
                            <Setter Property="ItemsSource" Value="{Binding Path=DataContext.Variables, ElementName=dataGridEx}" />
                    </Style>
                </DataGridComboBoxColumn.EditingElementStyle>
            </DataGridComboBoxColumn>

In this way everything works okay.

But I have custom control like IntelliSense instead of ComboBox. It is requires to use DataGridTemplateColumn with DataTemplates for CellTemplate and CellEditingTemplate. What Should I do in this case? Maybe I need to create custom DataGridComboBoxColumn?

Can you help me with my issue?