By exposing the DependencyProperty for your inner control you have solved half of the problem - ie you can set individual properties in xaml.
The next step is to have those property setters affect the child control.
There are two options to achieve that.
In your control template, define your child control and use Bindings on each property you want to set.
Define a container element in your parent control template and set it's content to your child whenever the dependency property changes.
Although both of these methods could work, you may find that the solution involving the least amount of code, and the greatest amount of flexibility, is to expose a Style property for your child control and apply that in the control template.
public class ParentControl : Control
{
public Style ChildControlStyle
{
get { return (Style)GetValue(ChildControlStyleProperty); }
set { SetValue(ChildControlStyleProperty, value); }
}
public static readonly DependencyProperty ChildControlStyleProperty =
DependencyProperty.Register("ChildControlStyle",
typeof(Style),
typeof(ParentControl),
new PropertyMetadata(null));
}
<Style TargetType="ParentControl">
<Setter Property="ChildControlStyle">
<Setter.Value>
<Style TargetType="ChildControl">
<!-- setters -->
</Style>
</Setter.Value>
</Setter>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="ParentControl">
<Grid>
<ChildControl Style="{TemplateBinding ChildControlStyle}" />
<!-- other stuff -->
</Grid>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>