I am not a joomla expert, but I think you can accomplish this by building 2 seperate templates. One for your 3 column layout, and one for your 2 column layout. Upload to your joomla installation via the Extention Manager.
Layout your modules on the landing (home) page using position beased on the 3 column template.
Layout your modules on the subsequent pages using the positions based on the 2 column template.
Give that a try and see how it works out for you.