the reason that disabling the horizontal scrollbar doesn't work is because in the default TreeView style, the scrollviwer's HorizontalScrollBarVisibility is set to Auto. What you can do is to create your own style and make it TemplateBinding to the parent.
<Style TargetType="sdk:TreeView">
<Setter Property="Background" Value="#FFFFFFFF"/>
<Setter Property="Foreground" Value="#FF000000"/>
<Setter Property="HorizontalContentAlignment" Value="Left"/>
<Setter Property="VerticalContentAlignment" Value="Top"/>
<Setter Property="Cursor" Value="Arrow"/>
<Setter Property="BorderThickness" Value="1"/>
<Setter Property="Padding" Value="1"/>
<Setter Property="BorderBrush" Value="#FF000000"/>
<Setter Property="IsTabStop" Value="True"/>
<Setter Property="TabNavigation" Value="Once"/>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="sdk:TreeView">
<Grid>
<VisualStateManager.VisualStateGroups>
<VisualStateGroup x:Name="CommonStates">
<VisualState x:Name="Normal"/>
<VisualState x:Name="MouseOver"/>
<VisualState x:Name="Pressed"/>
<VisualState x:Name="Disabled"/>
</VisualStateGroup>
<VisualStateGroup x:Name="FocusStates">
<VisualState x:Name="Unfocused"/>
<VisualState x:Name="Focused"/>
</VisualStateGroup>
<VisualStateGroup x:Name="ValidationStates">
<VisualState x:Name="Valid"/>
<VisualState x:Name="InvalidUnfocused">
<Storyboard>
<ObjectAnimationUsingKeyFrames Storyboard.TargetProperty="Visibility" Storyboard.TargetName="Validation">
<DiscreteObjectKeyFrame KeyTime="0" Value="Visible"/>
</ObjectAnimationUsingKeyFrames>
</Storyboard>
</VisualState>
<VisualState x:Name="InvalidFocused">
<Storyboard>
<ObjectAnimationUsingKeyFrames Storyboard.TargetProperty="Visibility" Storyboard.TargetName="Validation">
<DiscreteObjectKeyFrame KeyTime="0" Value="Visible"/>
</ObjectAnimationUsingKeyFrames>
<ObjectAnimationUsingKeyFrames Storyboard.TargetProperty="IsOpen" Storyboard.TargetName="ValidationToolTip">
<DiscreteObjectKeyFrame KeyTime="0">
<DiscreteObjectKeyFrame.Value>
<System:Boolean>True</System:Boolean>
</DiscreteObjectKeyFrame.Value>
</DiscreteObjectKeyFrame>
</ObjectAnimationUsingKeyFrames>
</Storyboard>
</VisualState>
</VisualStateGroup>
</VisualStateManager.VisualStateGroups>
<Border BorderBrush="{TemplateBinding BorderBrush}" BorderThickness="{TemplateBinding BorderThickness}" CornerRadius="2">
<Border Background="{TemplateBinding Background}" Margin="1" Padding="{TemplateBinding Padding}">
<ScrollViewer x:Name="ScrollViewer" BorderBrush="Transparent" BorderThickness="0" Background="{x:Null}" HorizontalScrollBarVisibility="{TemplateBinding ScrollViewer.HorizontalScrollBarVisibility}" IsTabStop="False" TabNavigation="Once" VerticalScrollBarVisibility="Auto">
<ItemsPresenter Margin="5"/>
</ScrollViewer>
</Border>
</Border>
<Border x:Name="Validation" BorderBrush="#FFDB000C" BorderThickness="{TemplateBinding BorderThickness}" Grid.Column="1" CornerRadius="2" Visibility="Collapsed">
<ToolTipService.ToolTip>
<ToolTip x:Name="ValidationToolTip" DataContext="{Binding RelativeSource={RelativeSource TemplatedParent}}" IsHitTestVisible="True" Placement="Right" PlacementTarget="{Binding RelativeSource={RelativeSource TemplatedParent}}" Template="{StaticResource CommonValidationToolTipTemplate}"/>
</ToolTipService.ToolTip>
<Grid Background="Transparent" HorizontalAlignment="Right" Height="10" Margin="0,-4,-4,0" VerticalAlignment="Top" Width="10">
<Path Data="M 1,0 L6,0 A 2,2 90 0 1 8,2 L8,7 Z" Fill="#FFDC000C" Margin="-1,3,0,0"/>
<Path Data="M 0,0 L2,0 L 8,6 L8,8" Fill="#FFFFFFFF" Margin="-1,3,0,0"/>
</Grid>
</Border>
</Grid>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
After applying this style you should have a horizontal scrollbar disabled treeview. Then you need to set the max width of your textblock to allow the ellipsis to show.
Please let me know if this helps. :)