<UserControl x:Class="ConnectionViewWithUC.DPCalculatorUC"
             xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
             xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
             xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006" 
             xmlns:d="http://schemas.microsoft.com/expression/blend/2008" 
             xmlns:local="clr-namespace:ConnectionViewWithUC"
             mc:Ignorable="d" d:DataContext="{x:Type local:ICalculator}" >
    <StackPanel Orientation="Horizontal">
        <TextBox VerticalAlignment="Center" 
                 Text="{Binding First, UpdateSourceTrigger=PropertyChanged}"
                 Margin="5" MinWidth="80"/>
        <ComboBox VerticalAlignment="Center"
                  ItemsSource="{Binding Operators}"
                  SelectedItem="{Binding SelectOperator}"
                  Margin="5" MinWidth="80"/>
        <TextBox Grid.Column="2" VerticalAlignment="Center" 
                 Text="{Binding Second, UpdateSourceTrigger=PropertyChanged}"
                 Margin="5"  MinWidth="80"/>
        <TextBlock Margin="5" VerticalAlignment="Center" Text="="/>
        <TextBox x:Name="tbResult" VerticalAlignment="Center" 
                 Text="{Binding Result, Mode=OneWay}" 
                 Margin="5" IsReadOnly="True" MinWidth="80"/>
    </StackPanel>
</UserControl>

namespace ConnectionViewWithUC
{
    /// <summary>
    /// Логика взаимодействия для DPCalculatorUC.xaml
    /// </summary>
    public partial class DPCalculatorUC : UserControl
    {
        public DPCalculatorUC()
        {
            InitializeComponent();
            Binding bind = new Binding();
            bind.Source = tbResult;
            bind.Path = new PropertyPath("Text");
            bind.Mode = BindingMode.TwoWay;
            SetBinding(ResultProperty, bind);
        }
 
 
 
        public int? Result
        {
            get { return (int?)GetValue(ResultProperty); }
            set { SetValue(ResultProperty, value); }
        }
 
        // Using a DependencyProperty as the backing store for Result.  This enables animation, styling, binding, etc...
        public static readonly DependencyProperty ResultProperty =
            DependencyProperty.Register("Result", typeof(int?), typeof(DPCalculatorUC), new PropertyMetadata(null));
 
    }
}

        <TextBox x:Name="tbResult" VerticalAlignment="Center" 
                 Text="{Binding Result, RelativeSource={RelativeSource FindAncestor, AncestorType={x:Type local:DPCalculatorUC}}}" 
                 Margin="5" IsReadOnly="True" MinWidth="80" />

<local:DPCalculatorUC ... Result="{Binding ResultMain, Source={StaticResource VM}}"/>

SetBinding(ResultProperty, bind);

namespace ConnectionViewWithUC
{

    public class UserControlResultDP : UserControl
    {
        public int? Result
        {
            get { return (int?)GetValue(ResultProperty); }
            set { throw new Exception("An attempt ot modify Read-Only property"); }
        }

        // Using a DependencyProperty as the backing store for Result.  This enables animation, styling, binding, etc...
        public static readonly DependencyProperty ResultProperty =
            DependencyProperty.Register("Result", typeof(int?), typeof(UserControlResultDP), new PropertyMetadata(null));

        protected int? PART_Result
        {
            get { return (int?)GetValue(PART_ResultProperty); }
            set { SetValue(PART_ResultProperty, value); }
        }

        // Using a DependencyProperty as the backing store for PART_Result.  This enables animation, styling, binding, etc...
        protected static readonly DependencyProperty PART_ResultProperty =
            DependencyProperty.Register("PART_Result", typeof(int?), typeof(UserControlResultDP), new PropertyMetadata(null, ChangeResult));

        private static void ChangeResult(DependencyObject d, DependencyPropertyChangedEventArgs e)
        {
            d.SetValue(ResultProperty, e.NewValue);
        }
    }
    /// <summary>
    /// Логика взаимодействия для DPCalculatorUC.xaml
    /// </summary>
    public partial class DPCalculatorUC : UserControlResultDP
    {
        public DPCalculatorUC()
        {
            InitializeComponent();
        }
    }
}

<local:UserControlResultDP x:Class="ConnectionViewWithUC.DPCalculatorUC"
             xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
             xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
             xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006" 
             xmlns:d="http://schemas.microsoft.com/expression/blend/2008" 
             xmlns:local="clr-namespace:ConnectionViewWithUC" PART_Result="{Binding Result}"
             mc:Ignorable="d" d:DataContext="{x:Type local:ICalculator}" >
    <StackPanel Orientation="Horizontal">
        <TextBox VerticalAlignment="Center" 
                 Text="{Binding First, UpdateSourceTrigger=PropertyChanged}"
                 Margin="5" MinWidth="80"/>
        <ComboBox VerticalAlignment="Center"
                  ItemsSource="{Binding Operators}"
                  SelectedItem="{Binding SelectOperator}"
                  Margin="5" MinWidth="80"/>
        <TextBox Grid.Column="2" VerticalAlignment="Center" 
                 Text="{Binding Second, UpdateSourceTrigger=PropertyChanged}"
                 Margin="5"  MinWidth="80"/>
        <TextBlock Margin="5" VerticalAlignment="Center" Text="="/>
        <TextBox VerticalAlignment="Center" 
                 Text="{Binding Result}" 
                 Margin="5" IsReadOnly="True" MinWidth="80" />
    </StackPanel>
</local:UserControlResultDP>

<Window x:Class="ConnectionViewWithUC.DPMainView"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:local="clr-namespace:ConnectionViewWithUC"
        SizeToContent="WidthAndHeight"
        mc:Ignorable="d" d:DataContext="{x:Type local:DPParentVM}" FontSize="18"
        Title="DPMainView (взаимодействие через DP свойство)">
    <Window.Resources>
        <local:DPParentVM x:Key="VM"/>
    </Window.Resources>
    <Window.DataContext>
        <Binding Mode="OneWay" Source="{StaticResource VM}"/>
    </Window.DataContext>
    <StackPanel>
        <TextBlock Margin="10">
            <Run Text="Результат вычисления:"/>
            <Run Text="{Binding ResultMain}"/>
        </TextBlock>
        <local:DPCalculatorUC DataContext="{Binding VMfromUC, Mode=OneWay}" 
                              Result="{Binding ResultMain, Mode=OneWayToSource, Source={StaticResource VM}}" />
    </StackPanel>
</Window>