Associate User Control with ViewModel class

When I define a DataTemplate inline, Visual Studio knows about the type I'm binding to, and properties in that type come up in autocomplete (for example in the code below I was able to select DisplayName from the autocomplete list inside the FirstViewModel template).

<DataTemplate DataType="{x:Type viewmodels:FirstViewModel}">
    <StackPanel >
        <Label Content="{Binding DisplayName}"/>
    </StackPanel>
</DataTemplate>

<DataTemplate DataType="{x:Type viewmodels:SecondViewModel}">
    <views:SecondView/>
</DataTemplate>

However, when the data template references an external control, as for SecondViewModel in the code above, when I'm in the file for the SecondView usercontrol, since it's just a control, the type isn't bound and the editor doesn't help me with anything.

I've tried wrapping my whole control (inside the UserControl element) in the same DataTemplate tag, but then my whole view just shows "System.Windows.DataTemplate".

<UserControl x:Class="Gui.Views.Tabs.ExamsTabViews.ExamInfoView"
             xmlns:vm="clr-namespace:Gui.ViewModels"
             mc:Ignorable="d" 
             d:DesignHeight="450" d:DesignWidth="800">

    <DataTemplate DataType="vm:ExamInfoViewModel">
        <DockPanel VerticalAlignment="Stretch" HorizontalAlignment="Stretch">

            <!-- contents of the template -->             

        </DockPanel>
    </DataTemplate>
</UserControl>

Is there a way to achieve this kind of binding for the editor?