If I was you, I'd look into dvc rental. I put your dates into dvcrequest.com (david's dvc rental) & consider these dvc villa options:
SARATOGA SPRINGS
$3808 treehouse
$2944 two bedroom
OLD KEY WEST
$2896 two bedroom
$4672 grand villa
WILDERNESS LODGE
$3632 two bedroom
ANIMAL KINGDOM LODGE
$2480 two bedroom value
$2960 two bedroom standard
BOARDWALK
$2960 two bedroom
I would hope for some special deal on one park per day tickets, otherwise you're looking at $2220 for five one park per day tickets for six. Another consideration would be a third party ticket vendor.
The dining plan prices before tax per person for 2018 are:
$52.49 quick service ($314.92 x 6 nights = $1889.52)
$75.49 standard ($452.94 x 6 nights = $2717.64)
$116.24 deluxe ($697.44 x 6 nights = $4184.64)
So, you could do a dvc rental + quick service dining plan + 5 day base tickets at a two bedroom old key west for just a few dollars over $7k. That is your entire budget though. I would strongly reconsider the dining plan, and look at getting
discount tickets. It's possible you could do two rooms at a resort, but a dvc villa would have a kitchen, enabling you to bring food or order groceries and eat some meals in the room to save on costs. It would also keep the family together, for better or worse. Knocking a night or two off your stay might also enable you to live a little more on your dime. It's possible you can get a good package deal through disney as the above poster noted, just explore your options!