You've got a few options. In case you weren't aware, you can buy many items from the resort itself. You can even fax your order ahead and they will stock your
DVC villa after you check-in. That's the expensive (but time-saving) way to go. A full list of items carried at each resort is available at the member web site.
There's a company called wegoshop.com that will handle the shopping for you for a nominal fee.
Unless you really need something for that night at CSR, I personally would just wait until you get into your villa. Run to the store in the evening, or some other time that won't totally disrupt your plans.
If you do need some items both days, then two stops is probably the way to go. Any chance you could bring some of the non-perishables in your luggage to avoid one of the trips?
There is a Publix that's only 5 minutes away from the Downtown Disney area, so it's not like you need to set aside 2 hours to get your shopping done. In fact, this particular Publix is right across the road from one of Disney's off-site outlet stores. If you're planning to buy any volume of souvenirs, it's a worthwile stop. All of the merchandise is official "Disney" stuff that represents either production overruns, discontinued or out-of-season items. Last May I bought a golf shirt with the logo of one of the Disney courses as a Father's Day gift. Original price was $54. I paid $26.