If you're only going to be there 6 nights, you might not want to get the tickets with the Water Parks option (the water parks are great in warm weather, but each one takes up most of a day). We can give you more advice if you tell us the ages of the kids. You can't just leave your brother, unless your folks hire a babysitter, but you can do the "baby swap" at the rides.
You have a hefty budget -- but money does go fast at WDW. If there's any way you can stay 8-10 nights, that would work out a lot better for your family, esp. coming from so far away. You could stay someplace less expensive in order to stay longer (altho having a kitchen can be a big help for a family).
Hopefully, you're not really going in just a couple of weeks (this Oct.) -- it will be helpful to have some time to plan; getting one guidebook is good, and reading a lot on this board, and intercot. com and allearsnet. com is also helpful.
WDW is huge -- even two weeks is not enough to see and do it all -- there are 4 main big parks, plus 2 waterparks, and other stuff. You can hit the highlights of the main parks in a day, but 2 is better, esp. for Epcot and Magic Kingdom (the one like
Disneyland).
Use PhotoPass a lot.
Try to go at a less crowded time -- after Thanksgiving and before Christmas break is good to see all the decoration, etc. Spring is also nice; the Flower Festival at Epcot in the spring is good, and you can overlap that with Star Wars weekends in May.
It's good to have a basic plan, but know that you can't do everything.
Ask all the questions you want here; you'll get a lot of advice.
Have fun!