Layering and grouping never seemed to make a difference for me (it still rerouted the connectors anyway), but changing the routing behavior of the placed object did. For Visio 2010 and 2013, the Behavior dialog is unfortunately and unnecessarily hidden by default. You have to customize the ribbon (
File > Options > Customize Ribbon or just right-click on the
Ribbon > Customize Ribbon), click the check mark next to the Developer item in the right-most tree view to enable it, and click
OK. Then select the shape you want to layer before and behind, click
Behavior on the ribbon (
Developer>Shape Design>Behavior), and on the Placement tab in the Placement behavior drop-down list choose
Do not lay out and route around.