Это просто, установите VerticalAlignment="Center"
с помощью 'StackPanel´
<Grid>
<Grid.RowDefinitions>
<RowDefinition Height="*"/>
<RowDefinition Height="Auto"/>
<RowDefinition Height="Auto"/>
<RowDefinition Height="*"/>
</Grid.RowDefinitions>
<TextBox TextWrapping="Wrap" Text="TextBox1 should be resized while moving the GridSplitter"/>
<GridSplitter HorizontalAlignment="Stretch" Height="5" Grid.Row="1" />
<StackPanel Grid.Row="2" Orientation="Horizontal" Background="Black" VerticalAlignment="Center">
<TextBlock Padding="5" Text="I want this black section have fixed height while moving the GridSplitter" Foreground="Aqua" VerticalAlignment="Center" />
</StackPanel>
<TextBox Grid.Row="3" TextWrapping="Wrap" Text="TextBox2 should be resized while moving the GridSplitter"/>
</Grid>