This could be a big job (tm)
You want to maintain a catlog of products on your own database and when the shopper chooses to checkout, you want to transfer all of those products onto the retailers shopping cart system. If that retailer doesn't provide an interface for this sort of mullarkey, then you're going to have to geenrate a series to page requests to the retailers site "select product x", "add to cart", "set quantity", "select product y", etc etc... it would be very, very slow and error prone.
What if the retailer changes/drops a product?
What if the retailer changes the price?
What if the retailer introduces some sort of a "3 for the price of 2" promotion?
What if one of your page requests to the retailer goes wrong for some reason?
And so on... and those are just the technical concerns, what about all the customer support. If I start off on your site I'm going to come to you when my product is lost, delayed or damaged.
Amazon allows you to code your own shop, but most retailers don't.