I believe the ItemsPanel property is responsible for the layout panel of the UXItemsControl, in your case you could set the UXItemsControl ItemsPanel to use StackPanel so each items will be added below the previous item.

<Intersoft:UXItemsControl HorizontalAlignment="Left" Margin="10,10,0,0" Name="uXItemsControl1" VerticalAlignment="Top">
    <Intersoft:UXItemsControl.ItemsPanel>
        <ItemsPanelTemplate>
            <StackPanel />
        </ItemsPanelTemplate>
    </Intersoft:UXItemsControl.ItemsPanel>
    <Intersoft:GroupBox Header="Group 1" >
        ...
    </Intersoft:GroupBox>
    <Intersoft:GroupBox Header="Group 2">
        ...
    </Intersoft:GroupBox>
</Intersoft:UXItemsControl>