Nested Binding With WPF

I am newbie to WPF and curious to know how to nested bind the properties in WPF. I have made a sample app for better understanding. Please find below the following scenario's.

Working Code:

UserControl1 >> MainWindow

Created a UserControl and included it in the mainWindow.

UserControl1.xaml

<StackPanel>
     <TextBox x:Name="text1" Text="{Binding MyTextUC1, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}"/>
     <TextBox />
</StackPanel>

UserControl1.xaml.cs

 public UserControl1()
 {
      InitializeComponent();
      this.DataContext = this;
 }

 public static readonly DependencyProperty MyTextUC1Property =
        DependencyProperty.Register("MyTextUC1", typeof(string),    typeof(UserControl1));

public string MyTextUC1
{
   get { return (string)GetValue(MyTextUC1Property); }
   set { SetValue(MyTextUC1Property, value); }
}

MainWindwo.xaml

<StackPanel>
    <local:UserControl1 x:Name="text1"/>
    <TextBlock Text="{Binding ElementName=text1, Path=MyTextUC1}" />
</StackPanel>

On running this, text changes in the TextBox of UserControl1 got reflected in TextBlock of MainWindow.

Not Working:

UserControl1 >> UserControl2 >> MainWindow

Created a UserControl(usercontrol1) and included it in another UserControl(usercontrol2) and then included the UserControl2 in mainWindow.

UserControl1.xaml & UserControl1.xaml.cs

//Same as Working Code

UserControl2.xaml

<Grid>
    <local:UserControl1 x:Name="text2" MyTextUC1="{Binding MyTextUC2,Mode=TwoWay,UpdateSourceTrigger=PropertyChanged}"/>
</Grid>

UserControl2.xaml.cs

 public UserControl2()
 {
     InitializeComponent();
     this.DataContext = this;
 }

 public static readonly DependencyProperty MyTextUC2Property =
     DependencyProperty.Register("MyTextUC2", typeof(string), typeof(UserControl2));       

 public string MyTextUC2
 {
     get { return (string)GetValue(MyTextUC2Property); }
     set { SetValue(MyTextUC2Property, value); }
 }

MainWindwo.xaml

<StackPanel>
    <local:UserControl2 x:Name="text1"/>   //UserControl2 contains UserControl1
    <TextBlock Text="{Binding ElementName=text1, Path=MyTextUC2}" />
</StackPanel>

On Running this, text changes in the TextBox of UserControl2 NOT REFLECTED in TextBlock of MainWindow.

I'm pretty sure that this is a basic thing in WPF and I may be implementing this in wrong way. Can someone suggest me where I am wrong? Thanks in advance.