Disneychix if connecting rooms are not available, they are not available. It is only a request, not a guarantee. No matter how much of a fuss you make that won't change the fact that the rooms are not available. Your response puzzles me. It seems that you believe that making a fuss will get you whatever you want - but that is not the case.
To OP, for your family I would suggest the Family Suites or the FW Cabins. as stated, connecting rooms can not be guaranteed. From Disney's perspective, in your case 1 parent could sleep with the children in each room - meaning you and DH could be separated with some of the kids in each room. With either the Family Suites or the Cabins you would be in one space with multiple rooms.
My choice would be the FW Cabins. They are more expensive but they are wonderful. You would have a full size, fully equipped kitchen. We also had breakfast in the Cabin, saving a lot of money. We also had cold drinks and snacks when we returned for a rest. You can put the kids to bed in the bedroom, close the door and have the Living Room for you and DH to relax in. And the campground is wonderful.
The one downside to the Cabins is that the transportation to the parks is more complicated here. You will need to take an Internal Bus to the bus stop to the Parks, and then a Park bus to the Park. Personally, once we figured out the internal bus routes we did not find this to be terrible.
Have a great trip, whatever you choose.