Hi James, We have a family of 7 so I can understand your desire to stretch your Disney dollar.
First, what I recommend is that your check out the various Disney Value Resorts. Click:
HERE . Your most economical option will be to rent 2 connecting, standard view Value rooms. With 2 adults and 4 children, you would be guaranteed connecting rooms. You'll have 2 showers, which as you know, is always great for a large family.
I answered a very similar question not to long ago, so rather than repeat all of that information I will provide you with a link:
SEE HERE . Sharing some of that information in a link allows me more space to tell you about other money saving options.
I'd recommend a Base Ticket as compared to a Park Hopper if you are trying to save money. There is more than enough to see in each Park to take up a whole day. In fact, we generally spend 2 days in each Park whenever possible. This will save you a considerable amount of money when it's for 6 people.
In addition, I suggest bringing snacks for the kids into the Parks. We always keep peanut-butter crackers, goldfish, etc on hand, as well as bottled water.
Keep an eye out for Special Offers. Often in the summer and early Fall, Disney offers it's immensely popular "Free Dining" promotion. As the name suggests, your entire family would receive Disney's basic dining plan for free with a magic-your-way package. This is a fantastic deal.
I hope this gives you some ideas. Please look over the links I sent and let me know if I can answer any other follow up questions you may have.
Kaylene