6 Days may be p.ushing it, but it also depends on when you go because of the changes in price for the rooms. When were you planning on your trip? Also where you are from would come into it, if you live within close driving distance, this is vastly different than booking a flight.
I'll edit this post with a general idea of costs.
EDIT: Since December 13th is your proposed check-in date (with check-out on the 18th driving home in the evening, unless you wanted to add an extra night to leave in the morning), you are looking at roughly $950 for the cheapest value at the All-Star Music Resort. This does not include tickets. If adding 7-day parkhopper tickets, it comes out to almost $2,150. I'll check and see if Passes would actually be cheaper.
EDIT 2: Electric Boogaloo: Scratch that, as it comes out to roughly $2,500.
So, Assuming you have All-Star Music Resort rooms, and 7-Day Parhopper tickets, it comes out to $2,150. This would leave you about $1,350 for cost of arrival (gas or flight), food, and any other expenses you would want to cover. Can you do it? Yes, if you are driving and are close. Will it be tight? Depends on your willingness to spend.
My advice would be to bring something to eat for breakfast in the room (The resort I chose in your scenario does not come with a mini-fridge, so plan ahead) and perhaps the occasional lunch. You have a young child and may need to stop back at the resort to rest mid-day anyway, so you can also bring things for this.
My other advice would be for souvenirs. If your grand-kids want something, think before you buy! Is it something that you could only get here? Is it something they will keep interest in past 5 minutes? That sort of thing. I hope I helped in any regard.