Hi Carolina,
I have a few ideas, each with a different budget to give you a few choices. While you mentioned not staying at a value resort, there is now a family suite located at All-Star Music. It has two rooms that are joined together, sleeps 6 (adults would have their own room), and has 2 bathrooms as well as a small kitchenette. The price is quite reasonable, too.
My second thought is the cabins at Ft. Wilderness. They, too, sleep 6 guests and have a small kitchen area, but there is only 1 bathroom. These are probably the middle range of costs.
Finally, there are several villas available throughout Walt Disney World that are part of the Disney Vacation Club. When rooms are not reserved for Disney Vacation Club members, they may be reserved by other guests. You'd be able to select from a 2 or 3 bedroom villa for a family of 6. These are considered deluxe accomodations, so the costs are more.