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

        WinFormsChildControl wfChildControl;
        WPFChildControlViewModel wpfChildControlViewModel;

        private void MainWindowControl_Loaded(object sender, RoutedEventArgs e)
        {
            WPFChildControl wpfChildControl = new WPFChildControl();
            wpfChildControlViewModel = new wpfChildControlViewModel();
            wpfChildControl.DataContext = wpfChildControlViewModel;
            // tiWpfChildControl - TabItem, содержащий wpfChildControl
            tiWpfChildControl.Content = wpfChildControl;

            wfChildControl = new wfChildControl();
            // wfh - WindowsFormsHost в TabItem
            wfh.Child = wfChildControl;
            wpfChildControlViewModel.PropertyChanged += WpfChildControlViewModel_PropertyChanged;
        }

        private void WpfChildControlViewModel_PropertyChanged(object sender, System.ComponentModel.PropertyChangedEventArgs e)
        {
            if (e.PropertyName == "CurrentDate")
            {
                wfChildControl.CurrentDate = (sender as WPFChildControlViewModel).CurrentDate;
                wpfChildControlViewModel.CurrentDate = (sender as WPFChildControlViewModel).CurrentDate;
            }
        }
    }

        private void MainWindowControl_Loaded(object sender, RoutedEventArgs e)
        {
            ...
            (this.DataContext as MainWindowControlViewModel).PropertyChanged += MainWindowControlViewModel_PropertyChanged;
        }

        private void MainWindowControlViewModel_PropertyChanged(object sender, System.ComponentModel.PropertyChangedEventArgs e)
        {
            if (e.PropertyName == "CurrentDate")
            {
                wfChildControl.CurrentDate = (sender as MainWindowControlViewModel).CurrentDate;
                wpfChildControlViewModel.CurrentDate = (sender as MainWindowControlViewModel).CurrentDate;
            }
        }