Hello, Jordana!
Yes, you absolutely can have a family member join you for a day in the parks, even though you're on the Disney Dining Plan. Just tell your server which person in your party will not be on the Dining Plan, and he or she will take care of it for you.
Depending on where you are, and what your taste buds enjoy, there are some really wonderful snack options out there. In Magic Kingdom Park, we love Casey's Corner for some great fries with cheese sauce, Main Street Bakery and Auntie Gravity's Galactic Goodies (ice cream, sundaes, floats and smoothies.) In Epcot, France has another wonderful bakery as well as a wonderful crepe kiosk. Disney's Hollywood Studios offers great ice cream at Dinosaur Gertie's, and Starring Rolls Cafe also offers great pastries as well. Quite a few of my Moms Panel friends also swear by the Carrot Cake Cookie, among other sweets, at The Writer's Stop, also in Disney's Hollywood Studios. Finally, in Disney's Animal Kingdom Park, my son and I fell in love with the slightly spicy Jalapeno Cheese Stuffed Pretzel, which is big enough for two.
If you happen to get to Downtown Disney, Goofy's Candy Co. also offers some delicious, gourmet items at the counter, which are available as snacks on the Dining Plan. Our kids favorite was a make-your-own chocolate-covered pretzel stick trio; what a hit!
To get an idea of the variety of food offered at Walt Disney World, check out a non-Disney site, allearsnet.com. There, you'll find fan-posted (and, thus, unofficial) menus and prices (subject to change) which will give you an idea of which shops you'd like to visit. Many, but not all, of these items are available as a snack on your Dining Plan. A good rule of thumb is that the snack will probably cost under $5 and will be non-protein based. Look for the DDP logo next to any item on the menus and signage while in the park.
Happy Eating!