Hi there Caroline,
Wow! A 15 night stay sounds incredibly AMAZING. I can't even describe how much I would enjoy a vacation like that! We actually stayed at Disney's Fort Wilderness Cabins a few years ago for 2 weeks and it was so much fun. With that amount of time, you'll really be able to slow down, and take your time without any rich or pressure to experience everything all of the parks have to offer... which is A LOT!!!
You are right, the maximum ticket length you can add to a vacation package is 10 days. We ran into this ourselves during our extended stay. I went ahead and booked the 14 nights with a 10-day ticket and then purchased the extra days separately. Now here's something else to consider... I am not sure if you have the Dining Plan or not, because if so, you couldn't do this, but have you considered booking a room-only reservation and then purchasing
Annual Passes? This may actually be more cost effective for you in the long-run. And as an Annual Passholder, you also have the option of adding the Dining Plan to a vacation package as long as you have purchased at least a 2-day ticket. And here's a bonus, you can then take those 2-day tickets and apply their value to the cost of your new Annual Passes.
I recommend taking these suggestions and sitting down to see what works best for your family when crunching all the numbers. I definitely think you may come out ahead with the Annual Pass route.
Best Wishes,
Amanda F.