It doesn't seem like the greatest way to set up an online shop via iframes. But...
You won't be able to rip the pages, unless you put in an awful lot of work. Or maybe I am thinking too much on it...
A run down of how both would work. An iframe is basically like a window or "portal" to another website. you could think of it as being a little web browser inside your web page almost. Requests made through the iframe are issued to the domain the iframe contents are hosted. So if you click "add to card" it will fire the request on the online shops domain.
If you rip the page contents, and load it from your domain, the requests made like "add to cart" will be issued to your domain. You will then have to create a way to transfer these requests to the online shop. As the script files and database are hosted there, it will be of no value on your hosting. You might be able to modify the links I guess so they fire to online shops domain and store the content data on your site, it depends how it works.
After reading your last post again, I think I understand how it works. A link to your domain and the online shop would be more helpful, though to see how it works.
My impression is you set up an online store with someone and it is hosted via a sub-domain or something similar? like
www.mugens-shop.onlineshophosting.com ? but you just want it to be
www.mugens-shop.com? If this is the case then what you could do is log in to where ever your domain name is managed and instead of the domain pointing to your hosting set it up as a redirect to the online shop.
so
www.mugens-shop.onlineshophosting.com will work as well as
www.mugens-shop.com.
Im probably thinking in the wrong direction, a link to the shop and to your site would be helpful to see what is going on.