Criar um controle personalizado com a combinação de vários controles em WPF C#

O Controlo

public class MyCustomControl : ItemsControl {

        static MyCustomControl() {
            DefaultStyleKeyProperty.OverrideMetadata(typeof(MyCustomControl), new FrameworkPropertyMetadata(typeof(MyCustomControl)));
        }

        private Button _addButton;
        private TextBox _textBox;
        private ListView _itemsView;

        public override void OnApplyTemplate() {
            this._addButton = this.GetTemplateChild("PART_AddButton") as Button;
            this._textBox = this.GetTemplateChild("PART_TextBox") as TextBox;
            this._itemsView = this.GetTemplateChild("PART_ListBox") as ListView;

            this._addButton.Click += (sender, args) => {
                (this.ItemsSource as IList<string>).Add(this._textBox.Text);
            };
            this._itemsView.ItemsSource = this.ItemsSource;
            base.OnApplyTemplate();
        }

        public ICommand DeleteCommand => new RelayCommand(x => { (this.ItemsSource as IList<string>).Remove((string)x); });
    }

O Modelo

 <Style TargetType="{x:Type local:MyCustomControl}">
    <Setter Property="Template">
        <Setter.Value>
            <ControlTemplate TargetType="{x:Type local:MyCustomControl}">
                <Border Background="{TemplateBinding Background}"
                        BorderBrush="{TemplateBinding BorderBrush}"
                        BorderThickness="{TemplateBinding BorderThickness}">
                    <Grid>
                        <Grid.RowDefinitions>
                            <RowDefinition Height="Auto" />
                            <RowDefinition Height="Auto" />
                        </Grid.RowDefinitions>
                        <Grid>
                            <Grid.ColumnDefinitions>
                                <ColumnDefinition Width="300" />
                                <ColumnDefinition Width="100" />
                            </Grid.ColumnDefinitions>
                            <TextBox x:Name="PART_TextBox" Grid.Column="0" />
                            <Button x:Name="PART_AddButton" Grid.Column="1" Content="Add" Margin="20,0" />
                        </Grid>
                        <ListView ItemsSource="{TemplateBinding ItemsSource}" Grid.Row="1" Margin="0,25" x:Name="PART_ListBox" HorizontalAlignment="Stretch" VerticalAlignment="Stretch" >
                            <ListView.ItemTemplate>
                                <DataTemplate>
                                    <StackPanel Orientation="Horizontal" HorizontalAlignment="Stretch">
                                        <TextBlock Text="{Binding}"/>
                                        <Button Content="X" Foreground="Red" 
                                                Command="{Binding RelativeSource={RelativeSource FindAncestor, AncestorType={x:Type local:MyCustomControl}}, Path=DeleteCommand}" 
                                                CommandParameter="{Binding}" Margin="10,0,0,0"></Button>
                                    </StackPanel>
                                </DataTemplate>
                            </ListView.ItemTemplate>
                        </ListView>
                    </Grid>
                </Border>
            </ControlTemplate>
        </Setter.Value>
    </Setter>
</Style>

RelayCommand

public class RelayCommand : ICommand
    {
        #region Fields

        private readonly Action<object> _execute;
        private readonly Predicate<object> _canExecute;

        #endregion // Fields

        #region Constructors

        public RelayCommand(Action<object> execute, Predicate<object> canExecute = null)
        {
            if (execute == null)
                throw new ArgumentNullException(nameof(execute));

            this._execute = execute;
            this._canExecute = canExecute;
        }

        #endregion // Constructors

        #region ICommand Members

        [DebuggerStepThrough]
        public bool CanExecute(object parameter)
        {
            return this._canExecute == null || this._canExecute(parameter);
        }

        public event EventHandler CanExecuteChanged {
            add { CommandManager.RequerySuggested += value; }
            remove { CommandManager.RequerySuggested -= value; }
        }

        public void Execute(object parameter)
        {
            this._execute(parameter);
        }

        #endregion // ICommand Members
    }

Utilização

 <local:MyCustomControl ItemsSource="{Binding Collection}"/>

Nota Não utilize um List como sua fonte ItemsSource. Em vez disso, use um ObservableCollection uma vez que notifica automaticamente a vista e você não tem que lidar com esse Update-Stuff