Hi Johnas
In our view add it to the main site. If you go for a split solution you dilute all the great work done from both sites. Adding a shopping section to the site will add more traffic to the XXX.com site and therefore will also bring in product specific links and recommendations.
There are some very learned colleagues here on Moz, who will be able to offer more thoughts about your thinking.
As always with SEO, distill the essence of your company and present it in a unique way. Unique in respect of making sure all reading material is written with your own words, with a moderate sprinkling of keywords.
Adding your ecommerce to the site enhances and leads the reader from reader to buyer
Hope that this helps
Bruce