Controlling DataTrigger ExitActions

Question 1

This can be achieved with IMultiValueConverter in place. Pass two bindings to it i.e. IsMouseOver and IsChecked.

Converter:

public class MyConverter : IMultiValueConverter
{
    public object Convert(object[] values, Type targetType, object parameter, 
                          CultureInfo culture)
    {
        bool isMouseOver = (bool)values[0];
        bool isChecked = (bool)values[1];

        return isChecked || isMouseOver;
    }

    public object[] ConvertBack(object value, Type[] targetTypes,
                                object parameter, CultureInfo culture)
    {
        throw new NotImplementedException();
    }
}

XAML:

<DataTrigger Value="True">
   <DataTrigger.Binding>
      <MultiBinding Converter="{StaticResource MyConverter}">
         <Binding Path="IsMouseOver" ElementName="imageGrid"/>
         <Binding Path="IsChecked" RelativeSource="{RelativeSource Self}"/>
      </MultiBinding>
   </DataTrigger.Binding>
   <!-- Rest same trigger -->
</DataTrigger>

Of course you need to add MyValueConverter instance as resource in your XAML file.

Question 2

Update February 26th: In your Style that is not working, you reference the checkbox the wrong way. ElementName can only be used in a binding if the target control was given a name and is accessible within the current WPF XAML namescope (you can learn about XAML namescopes here).

You should use a relative source within your binding to reference the CheckBox correctly: RelativeSource={RelativeSource Self}. The following ListView style shows the whole example:

<Style x:Key="ListViewItemStyle" TargetType="{x:Type ListViewItem}">
    <Setter Property="Template">
        <Setter.Value>
            <ControlTemplate>
                <Border Background="{TemplateBinding Background}">
                    <Grid Margin="{TemplateBinding Padding}">
                        <Grid.ColumnDefinitions>
                            <ColumnDefinition Width="150" />
                            <ColumnDefinition />
                        </Grid.ColumnDefinitions>
                        <TextBlock Text="{Binding Name}" TextTrimming="CharacterEllipsis" />
                        <CheckBox IsChecked="{Binding IsSelected}" Grid.Column="1">
                            <CheckBox.Style>
                                <Style TargetType="{x:Type CheckBox}">
                                    <Setter Property="Opacity" Value="0.0" />
                                    <Style.Triggers>
                                        <MultiDataTrigger>
                                            <MultiDataTrigger.Conditions>
                                                <Condition Binding="{Binding Path=IsMouseOver, RelativeSource={RelativeSource AncestorType=ListBoxItem}}"
                                                        Value="False" />
                                                <Condition Binding="{Binding Path=IsChecked, RelativeSource={RelativeSource Self}}"
                                                        Value="False" />
                                            </MultiDataTrigger.Conditions>
                                            <MultiDataTrigger.EnterActions>
                                                <BeginStoryboard>
                                                    <Storyboard>
                                                        <DoubleAnimation Storyboard.TargetProperty="Opacity"
                                                                        To="0.0" Duration="0:0:0.4" />
                                                    </Storyboard>
                                                </BeginStoryboard>
                                            </MultiDataTrigger.EnterActions>
                                            <MultiDataTrigger.ExitActions>
                                                <BeginStoryboard>
                                                    <Storyboard>
                                                        <DoubleAnimation Storyboard.TargetProperty="Opacity"
                                                                        To="1.0" Duration="0:0:0.4" />
                                                    </Storyboard>
                                                </BeginStoryboard>
                                            </MultiDataTrigger.ExitActions>
                                        </MultiDataTrigger>
                                    </Style.Triggers>
                                </Style>
                            </CheckBox.Style>
                        </CheckBox>
                    </Grid>
                </Border>
            </ControlTemplate>
        </Setter.Value>
    </Setter>
</Style>

You can download a working example from here (DropBox link).

Original Answer: You can use a MultiDataTrigger within your style to accomplish the behavior you want. Have a look at the following code:

<CheckBox Grid.Column="1" VerticalAlignment="Center" HorizontalAlignment="Center" Content="Check Me" Name="CheckBox">
    <CheckBox.Style>
        <Style TargetType="{x:Type CheckBox}">
            <Setter Property="Opacity" Value="0.0" />
            <Style.Triggers>
                <MultiDataTrigger>
                    <MultiDataTrigger.Conditions>
                        <Condition Binding="{Binding ElementName=Rectangle, Path=IsMouseOver}" Value="False" />
                        <Condition Binding="{Binding ElementName=CheckBox, Path=IsChecked}" Value="False" />
                    </MultiDataTrigger.Conditions>
                    <MultiDataTrigger.EnterActions>
                        <BeginStoryboard>
                            <Storyboard>
                                <DoubleAnimation Storyboard.TargetProperty="Opacity"
                                                 To="0.0"
                                                 Duration="0:0:0.4"
                                                 BeginTime="0:0:0.5" />
                            </Storyboard>
                        </BeginStoryboard>
                    </MultiDataTrigger.EnterActions>
                    <MultiDataTrigger.ExitActions>
                        <BeginStoryboard>
                            <Storyboard>
                                <DoubleAnimation Storyboard.TargetProperty="Opacity"
                                                 To="1.0"
                                                 Duration="0:0:0.4" />
                            </Storyboard>
                        </BeginStoryboard>
                    </MultiDataTrigger.ExitActions>
                </MultiDataTrigger>
            </Style.Triggers>
        </Style>
    </CheckBox.Style>
</CheckBox>

A MultiDataTrigger is used to describe two conditions that have to be true for the enter actions to be executed. In this case I choose that the IsMouseOver property of a rectangle as well as the IsChecked property of the checkbox must both be false. Thus the checkbox is faded in when the mouse is over the rectangle and stays visible when it becomes checked.

You can download my full sample here (it's a Dropbox link).

Hope this helps you. If you have any questions, please feel free to leave a comment.