Well I can't give you info particular to your family size but we went this past Sept between hurricanes. Most of the parks were pretty empty. We opened AK and left right after the parade at 4:30pm. I feel like we missed so much. There is a lot to do at AK. The Lion King show and the safari alone will take about 2hrs even if the lines are short. We did it the very last day because I heard it doesn't take long. If we would have done it sooner in the trip, we would have went back again.
I would suggest starting at MK, it is great walking down Main Street your first full day there. The rest of the days I would try and split them up - like AK in AM, Epcot at night. I personally feel this rejuvinates the whole crowd, even if you don't take a long break between parks. The one thing, I think people do when they are first there is rush rush and it is the little things at the parks that are so fun - don't stress yourself out, the kids will do that for you, LOL!! Go there with an open mind and soak it all in.
When planning your days in advance, take into consideration, the parade times, the fireworks, Extra Magic hours and regular park hours - you won't know those times for a few months so don't worry too much at this point. Utilize FASTPASS - you will get more done. Also, go early in the AM - even if it means you need to take the 4 and 5 yr olds back for a rest in the afternoon. They will last longer overall, esp at night. My 3 yr old dd closed all the parks with energy after her daily rests/naps. The one thing I would probably do is have your 15 yr old dd go with one of the adults on rides during any of the day parades at AK, MGM or MK, unless she truly loves the characters. The lines are so much shorter then and she can ride while the younger ones are resting and watching the parade. Same if you take the kids back during the day, let someone keep your 15 yr old out to enjoy grown up time. Maybe you can go with her and enjoy some of the rides too one day. Let DH and/or parents watch the younger ones one afternoon or night!!
Also - split up Epcot, if not you will be walking A LOT!! Personally we like doing Future World one day then heading back to MK at night, resting on the monorail. Then go back another night, usually after AK to do World Showcase/Illuminations. The yonger ones probably won't like World Showcase that much, we took our dd there one night for about 3 hrs and that was plenty for her! She was also scared of how noisy Illuminations is and she normally likes fireworks. Keep that in mind.
My main suggestion is to leave your last day there open for wherever you decide you need to visit again. Depending on crowds, hours and times it could really be any park - it is subjective to your needs. Try and go back to MK the last night though. We always start and end there EVERYTIME. It just feels right.
I could go on and on - you will find so many suggestions here. I love this board. Feel free to PM me for anything specific...
Good Luck!!