Hi Mirrornl, if interlinking of the 2 sites were a big issue, I'm pretty sure the second domain would have been hit too and harder, as it's domain authority is much lower. According to Opensite Explorer, the main website has an authority of 75 and the domain with the shopping cart, an authority of 35.
The drop happened the day of Penguin, so it's definitely related to links. I don't personally believe internal links could trigger such a response from Penguin. Plus, I cannot see any potential issues with their internal link structure.