Вы можете написать ControlTemplate для UserControl, который просто игнорирует свойство VerticalContentAlignment. Затем привяжите VerticalAlignment TextBox к свойству VerticalContentAlignment в UserControl, например, привязкой RelativeSource.
<UserControl ...>
<UserControl.Template>
<ControlTemplate TargetType="UserControl">
<ContentPresenter
HorizontalAlignment="{TemplateBinding HorizontalContentAlignment}"/>
</ControlTemplate>
</UserControl.Template>
<Grid Background="AliceBlue">
<TextBlock
Text="Hello"
VerticalAlignment="{Binding VerticalContentAlignment,
RelativeSource={RelativeSource AncestorType=UserControl}}"/>
</Grid>
</UserControl>
Контрольный пример:
<Grid>
<local:MyUserControl
Height="100"
VerticalAlignment="Center"
VerticalContentAlignment="Bottom"/>
</Grid>