<UserControl 
  x:Class="UntitledProject1.BaseUserControl"
  xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
  xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
  Height="300" Width="300"
  >
  
  <Grid>
    <WrapPanel>
      <Button x:Name="btnBase">test button</Button>
    </WrapPanel>
  </Grid>
</UserControl>

public partial class BaseUserControl : UserControl
{
    public BaseUserControl()
    {
        InitializeComponent();
    }
}

// ===========================================================

public partial class UserControl1 : BaseUserControl
{
    public UserControl1()
    {
        InitializeComponent();
        btnBase.Width = 100;
        btnBase.Height = 100;
    }
}

// ===========================================================

public partial class BaseUC : UserControl
{
    private ObservableCollection<string> _dataSource = new ObservableCollection<string>();

    public ObservableCollection<string> DataSource
    {
        get { return _dataSource; }
        set { _dataSource = value; }
    }
}

// ===========================================================

<local:BaseUC
  x:Class="UntitledProject1.UserControl2"
  xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
  xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
  xmlns:local="clr-namespace:UntitledProject1"
  Height="300" Width="300"
>
  
  <Grid Background="Yellow">
    <ItemsControl x:Name="testData" />
  </Grid>
</local:BaseUC>

public partial class UserControl2 : BaseUC
{
    public UserControl2()
    {
        InitializeComponent();
        this.DataSource.Add("aaa");
        this.DataSource.Add("bbb");
        testData.ItemsSource = this.DataSource;
    }
}

// ===========================================================

<Window
  xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
  xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
  x:Class="UntitledProject1.Window1"
  x:Name="Window"
  Title="Window1"
  Width="640" Height="480"
  >

  <Grid x:Name="LayoutRoot" Background="#FF000000">
    <Grid.RowDefinitions>
      <RowDefinition Height="Auto" />
      <RowDefinition Height="*" />
    </Grid.RowDefinitions>
    <WrapPanel>
      <Button Width="100" VerticalAlignment="Top" Content="Button" Click="Button_Click_1" />
      <Button Width="100" VerticalAlignment="Bottom" Content="Button" Click="Button_Click" />
    </WrapPanel>
    
    <WrapPanel x:Name="panel" Grid.Row="1">      
    </WrapPanel>
  </Grid>
</Window>

public partial class Window1
{
    public Window1()
    {
        this.InitializeComponent();
    }

    private void Button_Click(object sender, RoutedEventArgs e)
    {
        UserControl uc = new UserControl2();
        panel.Children.Add(uc);
    }

    private void Button_Click_1(object sender, RoutedEventArgs e)
    {
        UserControl uc = new UserControl1();
        panel.Children.Add(uc);
    }
}