The difference with the OP situation is that the amount of points during your week and the week they are looking for is huge. A week during October in the value studio is 69 points, whereas the OP is looking for the premier season which is 118 points for the week. At a rate of $12 a point (the average I've seen), your vacation would be $828, which would be little over $100 a night. The OP's week would be $1416 if they were even able to get a value studio during that week at all (I am assuming that by now that week is gone to the owners of AKV who booked at 11 months).
As for the OP's original question, I do think the value studios would be big enough for 2 adults and 2 children. Just all depends if it's worth the money to pay that for the room for the OP!