WPF Binding to ElementName inside ItemsControl

I have a checkbox, and an ItemsControl populating several DataGrids the following way:

<Checkbox Content="Birthday Column Visible" x:Name="UI_BirthdayVisibleCB" />

<ItemsControl  ItemsSource="{Binding Path=ParentsCollection}">
   <ItemsControl.ItemTemplate>
      <DataTemplate>
         <DataGrid  AutoGenerateColumns="False" ItemsSource="{Binding Children}">
            <DataGrid.Columns>
                <DataGridTemplateColumn Header="Birthday" Width="120" Visibility="{Binding IsChecked, ElementName=UI_BirthdayVisibleCB, Converter={StaticResource BoolToVis}}" >
...
               </DataGridTemplateColumn>
            </DataGrid.Columns>
         </DataGrid>
</Rest of closing tags>

This creates binding output errors as it tries to find IsChecked on the DataGridTemplateColumn. If I try to search for a Relative Ancestor I receive the exception:

Binding.RelativeSource cannot be set while using Binding.ElementName.

I have a ViewModel, and stick to MVVM mostly, but in this case I'd really like to keep the column visibilities on the View layer. Note that BoolToVis just converts Boolean to Visibility.

Edit

Here is an example of what I'm trying to do:

 <DataGridTemplateColumn Header="Birthday" Visibility="{Binding RelativeSource={RelativeSource FindAncestor, AncestorType={x:Type local:MyView} }, Path=IsChecked, ElementName=UI_BirthdayVisibleCB, Converter={StaticResource BoolToVis}}" />

It compiles but doesn't run however, it throws the exception above.