How to include an external website

[JohnnyB]

You would most likely have to use iframes.  There is a built in module to use for this, or you could just customized a template with iframes and assign it to the pages used for the shopping site.

[Pierre M.]

I suggest to have a nice URL plan, some for content (with CMSms) and some for commerce (with the other PHP software). Try to use a similar looking theme/template. And then you can have links from one to the other.
But I won't suggest to use frames, iframes and alike.

I recommend to "include" by templating, not by ugly mixing. It is technically simpler and safer.

PM