WolfGang Puck's Express is located on both sides...The one on the Marketplace side is by itself...the one on the West Side is with the restaurants. You can eat outside at both of the Express locations, but they are "express" while they offer great food, they are still quick service. No reservations required.
Wolf Gang Puck's Cafe is the actual sit down with the family, no dress code, good full service meal. You can eat outside at this one as well. They have a fairly large patio on the side and the back of the restaurant. They do suggest reservations for this one which you would need to book through group dining (since you have more than 8 people) at 407-939-7707
Wolf Gang Puck's "The Dining Room" is the higher end option. It is on the 2nd floor of the Cafe. It has a dress code, resort casual (men must wear collared shirts...etc). This one requires reservations but you could call 407-WDW-DINE for that one as they consider a group over 13.
I think you are looking to eat at the Cafe. The food is really good and the outside seating is nice... I have never eaten in the restaurant, we are always on the patio. For vegiterian needs you don't need to call ahead, they can accomodate you right there, just let the server know when you arrive.