If I've understood your structure correctly, something like this should work:
<Window ...>
<Window.Resources>
<CollectionViewSource x:Key="Collection2View" Source="{Binding Path=Object2.Collection2}" />
</Window.Resources>
<ListView ItemsSource="{Binding Object1.Collection1}" ...>
<ListView.View>
<GridView>
<GridView.Columns>
<GridViewColumn Header="Collection 2">
<GridViewColumn.CellTemplate>
<DataTemplate>
<ComboBox ItemsSource="{StaticResource Collection2View}"/>
</DataTemplate>
</GridViewColumn.CellTemplate>
</GridViewColumn>