The layout of a Python Addin can be changed by editing/updating the config.xml file.
Also trying to get my head and hands around the various ways ArcGIS can use Python via scripts (.py), ArcToolbox toolboxes (.tbx), Python toolboxes (.pyt), including Python Addins (.py and .xml).
Using the Python Addin Assistant (PAA) will generate a config.xml file that you can later update/edit via the PAA, or an editor to change the layout (e.g., to nest a tool under a menu, and the menu in a toolbox...the PAA UI seems to only allow buttons or menus under menus).
Here are screen shots of the nesting/layout edit i am trying to describe:


And here's a sample of the config.xml edit i am trying to describe:
<ESRI.Configuration xmlns="http://schemas.esri.com/Desktop/AddIns" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<Name>MouseClickTools</Name>
<AddInID>{bd14488e-47a2-4ab4-89d1-45aa9a8ef0d2}</AddInID>
<Description>Mouse Click Tools</Description>
<Version>0.1</Version>
<Image />
<Author>Author</Author>
<Company>Company</Company>
<Date>06/04/2014</Date>
<Targets>
<Target name="Desktop" version="10.2" />
</Targets>
<AddIn language="PYTHON" library="MouseClick2_addin.py" namespace="MouseClick2_addin">
<ArcMap>
<Commands>
<Tool caption="Window Click Tool" category="MouseClick" class="McToolClass_Win" id="MouseClick_addin.mcToolWin" image="Images\3DAnalystInterpolatePoint16.png" message="Click in Data Frame to see window coordinates." tip="Shows window coordinates."><Help heading="Windows Click Tool">Windows Click Tool</Help></Tool> <!-- 1st tool, defined -->
<Tool caption="Map Click Tool" category="MouseClick" class="McToolClass_Map" id="MouseClick_addin.mcToolMap" image="Images\3DAnalystInterpolatePoint16.png" message="Click in Data Frame to see map coordinates." tip="Shows map coordinates."><Help heading="Map Click Tool">Map Click Tool</Help></Tool> <!-- 2nd tool, defined -->
</Commands>
<Toolbars>
<Toolbar caption="Click Tools" category="MouseClick" id="MouseClick_addin.mcToolbar" showInitially="true"> <!-- 1st toolbar, defined -->
<Items>
<Menu refID="MouseClick_addin.mcMenu" /> <!-- 1st menu nested in toolbar-->
<Menu refID="MouseClick_addin.mcMenu" /> <!-- 1st menu, added a 2nd time, just for layout editing illustration -->
</Items>
</Toolbar>
</Toolbars>
<Menus>
<Menu caption="Click Clickity Click" category="MouseClick" id="MouseClick_addin.mcMenu" isRootMenu="true" isShortcutMenu="false" separator="true"> <!-- 1st menu, defined -->
<Items>
<Tool refID="MouseClick_addin.mcToolWin" /> <!-- 1st tool, nested in menu-->
<Tool refID="MouseClick_addin.mcToolMap" /> <!-- 2nd tool, nested in menu -->
</Items>
</Menu>
</Menus>
</ArcMap>
</AddIn>