WPF

// Stores the value of the DP IsPaneExpanded during initialization. See
// comments in the DP IsPaneExpanded 
private bool _isPaneExpanded = false;

// Set to true after the control has finished initializing
private bool _isInitialized = false;

public static readonly DependencyProperty IsPaneExpandedProperty =
            DependencyProperty.Register("IsPaneExpanded",
            typeof(bool),
            typeof(NavigationPane),
            new PropertyMetadata(false, new PropertyChangedCallback(OnIsPaneExpandedChanged)));

public bool IsPaneExpanded
{
    get { return (bool)GetValue(IsPaneExpandedProperty); }
    set { SetValue(IsPaneExpandedProperty, value); }
}

private static async void OnIsPaneExpandedChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
{
    var control = (NavigationPane)d;

    if (!control._isInitialized)
    {
        // If here, the control is still being initialized. Store the
        // IsPaneExpanded setting for later use when the control's init
        // has finished
        control._isPaneExpanded = control.IsPaneExpanded;

        // Since the control is not loaded, there is nothing to show. But
        // since the IsExpanded can be set from the Window, and it's bound,
        // it's possible for the expander arrow to show open even though
        // there's nothing there. So force the expander to show as collapsed
        control.IsPaneExpanded = false;
    }
    else
    {
        // If here, the control has already been initialized, so go ahead
        // and call load. If here, the user clicked the expander arrow.
        if (control.IsPaneExpanded)
        {
            await control.Load();
        }
    }
}

private async void NavigationPane_Initialized(object? sender, EventArgs e)
{
    // If the control's IsPaneExpanded was set from the parent, then
    // the IsPandedExpanded DP would have set _isPaneExpanded = true.
    if (_isPaneExpanded) <==================================================== PROBLEM 1 HERE
    {
        // Now that the control has finished initializing, go ahead
        // and call load

        <=============================== PROBLEM 2 HERE. HOW DO YOU FORCE THE EXPANDER TO SHOW AS OPEN BEFORE LOAD
        await Load();
    }

    _isInitialized = true;
}

<ResourceDictionary xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
                    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
                    xmlns:local="clr-namespace:BubblingEventsDemo"
                    xmlns:i="http://schemas.microsoft.com/xaml/behaviors">

    <Style TargetType="{x:Type local:InnerControl}">
        <Setter Property="Template">
            <Setter.Value>
                <ControlTemplate TargetType="{x:Type local:InnerControl}">

                    <Border Background="{TemplateBinding Background}"
                            BorderBrush="{TemplateBinding BorderBrush}"
                            BorderThickness="{TemplateBinding BorderThickness}">

                        <Button Content="Click Me"
                                Height="32"
                                Width="75">

                            <i:Interaction.Triggers>
                                <i:EventTrigger EventName="Click">
                                    <i:InvokeCommandAction Command="{Binding ButtonClickedCommand, 
                                                            RelativeSource={RelativeSource TemplatedParent}}"/>
                                </i:EventTrigger>
                            </i:Interaction.Triggers>

                        </Button>

                    </Border>

                </ControlTemplate>
            </Setter.Value>
        </Setter>
    </Style>

    <Style TargetType="{x:Type local:OuterControl}">
        <Setter Property="Template">
            <Setter.Value>
                <ControlTemplate TargetType="{x:Type local:OuterControl}">

                    <Border Background="{TemplateBinding Background}"
                            BorderBrush="{TemplateBinding BorderBrush}"
                            BorderThickness="{TemplateBinding BorderThickness}">

                        <local:InnerControl Height="100"
                                            Width="150"
                                            Background="LightBlue"/>

                    </Border>

                </ControlTemplate>
            </Setter.Value>
        </Setter>
    </Style>

</ResourceDictionary>

using CommunityToolkit.Mvvm.Input;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Input;

namespace BubblingEventsDemo
{
    public class InnerControl : Control
    {
        private ICommand? _ButtonClickedCommand;
        public ICommand ButtonClickedCommand
        {
            get
            {
                if (_ButtonClickedCommand == null)
                    _ButtonClickedCommand = new RelayCommand(ButtonClickedExecuted, ButtonClickedCanExecute);
                return _ButtonClickedCommand;
            }
        }

        public static readonly RoutedEvent ButtonClickedEvent =
                    EventManager.RegisterRoutedEvent("ButtonClicked",
                    RoutingStrategy.Bubble,
                    typeof(RoutedEventHandler),
                    typeof(InnerControl));

        public event RoutedEventHandler ButtonClicked
        {
            add { AddHandler(ButtonClickedEvent, value); }
            remove { RemoveHandler(ButtonClickedEvent, value); }
        }

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

        private bool ButtonClickedCanExecute()
        {
            return true;
        }

        private void ButtonClickedExecuted()
        {
            RaiseEvent(new RoutedEventArgs(ButtonClickedEvent));
        }
    }
}

<Window x:Class="BubblingEventsDemo.UI.MainWindowView"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:i="http://schemas.microsoft.com/xaml/behaviors"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:ctrls="clr-namespace:BubblingEventsDemo;assembly=BubblingEventsDemo"
        mc:Ignorable="d"
        Title="MainWindow" 
        Height="450" 
        Width="800">

    <Grid>

        <ctrls:OuterControl Background="Tan"
                            Height="225"
                            Width="300"
                            ctrls:InnerControl.ButtonClicked="OuterControl_ButtonClicked"> <==== THIS CATCHES THE EVENT IN THE WINDOW'S CODE BEHIND

            <i:Interaction.Triggers>

                WHAT I WANT IS TO HANDLE IT IN THE VIEW MODEL. WHAT GOES HERE IN 'EventName'?

                <i:EventTrigger EventName="OuterControl_ButtonClicked">
                    <i:InvokeCommandAction Command="{Binding ButtonClickedCommand, RelativeSource={RelativeSource TemplatedParent}}"/>
                </i:EventTrigger>
            </i:Interaction.Triggers>

        </ctrls:OuterControl>

    </Grid>

</Window>

<Expander Padding="{Binding Padding, RelativeSource={RelativeSource TemplatedParent}}"
        Margin="{Binding Margin, RelativeSource={RelativeSource TemplatedParent}}"
        BorderBrush="{Binding BorderBrush, RelativeSource={RelativeSource TemplatedParent}}"
        BorderThickness="{Binding BorderThickness, RelativeSource={RelativeSource TemplatedParent}}"
        ScrollViewer.HorizontalScrollBarVisibility="Auto"
        ScrollViewer.VerticalScrollBarVisibility="Auto"
        IsExpanded="{Binding IsPaneExpanded, RelativeSource={RelativeSource TemplatedParent}}">

    <Expander.Header>

        <Grid>

            <Grid.ColumnDefinitions>
                <ColumnDefinition Width="*"/>
                <ColumnDefinition Width="Auto"/>
            </Grid.ColumnDefinitions>

            <TextBlock Text="{Binding Header}"
                    HorizontalAlignment="Left"
                    VerticalAlignment="Center"
                    Margin="1"/>

            <Button Grid.Column="1"
                    Height="18"
                    Width="18"
                    Margin="0,1,1,1"/>

        </Grid>

    </Expander.Header>

    <CONTENT REMOVED FOR BREVITY>

</Expander>