I believe that you can use a trigger in the style to achieve this. You can place your image left aligned and in the trigger change that to right.
Something similar to:
<Style.Triggers>
    <Trigger Property="ItemsControl.AlternationIndex" Value="1">
           <!-- Change image position here -->
    </Trigger>
<Style.Triggers>
More information about how to use AlternationIndex here.
Edit - Working Sample
    <Style TargetType="ListViewItem">
        <Setter Property="Template">
            <Setter.Value>
                <ControlTemplate TargetType="{x:Type ListViewItem}">
                        <DockPanel>
                            <Image Source="/WpfApplication;component/Images/TestImage.jpg" DockPanel.Dock="Left" x:Name="rowImage"/>
                            <TextBlock Text="Testing..." Background="{TemplateBinding Background}"/>
                        </DockPanel>
                    <ControlTemplate.Triggers>
                        <Trigger Property="ItemsControl.AlternationIndex" Value="1">
                            <Setter Property="DockPanel.Dock" TargetName="rowImage" Value="Right" />
                        </Trigger>
                    </ControlTemplate.Triggers>
                </ControlTemplate>
            </Setter.Value>
        </Setter>
    </Style>