2:40 p.m. on July 26, 2012 (EDT)
Hi Jonathan, seems like you will be hauling alot of stuff since your kids are fairly young, before going into details about gear, know that water and food for all these people are probably going to be the bulk of your weight, so get familiar with managing those as you go on your trips. Dehydrated food for me seems to be the way to go right now (for me), I'm getting into making them on my own, you should look into that also, I posted a topic here a while back about that.
Now related to gear, the 3 things that will weight the most will be first your tent, then sleeping bag/sleeping pad combo, and then your backpack, the difference between products with those will be in pounds, rather than ounces.
You seem to have your backpacks already, I would not have recommended external frame, but stay with what you have until you decide to change for something better.
For sleeping bag I currently use the Kelty Cosmic Down, you can find them anywhere from $50-$100 bucks online, they are lightweight, durable, and compress well, you can use that model to compare to other bags as you shop. When selecting a sleeping bag I recommend getting something rated 20 degrees with a full length zipper to control temperature, I've slept anywhere from 20-60F with my 20 degree bag super comfortably, I could probably go into single digits with it by adding layer and using different sleeping pad, I just never really encountered those temperatures with that bag. Sleeping pad is a little harder, you first gotta decide if you are going for an air pad or a closed cell foam pad, depending on how you sleep that will matter alot, a good cheap foam pad that is lightweight are the Thermarest Z-Lite, as for air mats, you should really just go to a store and try as many as you can to see which are most comfortable for you, temperature rating is also something to think about.
Now for a tent, boy there are so many out there with such crazy price range ($5-$1000) it's hard to recommend one, you can either go with two 2 person tents, or one 3 person and one 2 person tent, or even just a 4 person tent, all depends on your body frame. I'm slim but tall, my wife is skinny and short, we fit just fine in a 2 person tent, but if I go with my brother who is 6ft4 and 240lbs we need something bigger, give us a price range and what you are looking to get and we can help you more on this selection, also note that this will probably be your most expensive single purchase, may require a thread on its own.
Stove and cookset now, if I were you, not saying that's what everyone will agree or that is what you should do, but if I was on your shoes I would sell the MSR Whisperlite for as much as you can get, keep the Snowpeak Litemax(which is an amazing stove), build yourself an alcohol fuel stove which is pretty much free(and easy, search youtube), and use the money from the whisperlite to get a nice cook set, the best in my opinion are from MSR, Snowpeak and Evernew. Go for a titanium set if you are bringing dehydraded food and just boiling water, go for aluminum if you are doing gourmet cooking, you should consider getting a skillet and cookware with nonstick coating depending on what you are going to eat. I use the MSR Quick pot set and the MSR quick skillet just so you can compare to what your get, and btw I love them! Another option is cooking over fire, some people do it, some don't, it's not as convenient but you could boil water, make hotdogs, etc...
You seem to have the water filter ready, I never used that one, but if it works to filter bacteria then go for it, invest your money on something else until you know what you want.
Other things you are missing:
Get a good compass, not a cheapo one, one fully featured less than $10.
Get a rope to hang your food from the bears and rodents.
Get a wash kit with TP, Bio degradable soap, wet wipes, traveler toothbrush and toothpaste(the mini ones), maybe some gold bond body powder if you are planning on going over 2 nights, and a shovel if your soil is hard to dig with branches.
Make your own first aid kit with things you need for you and your family, don't forget some chewable pepto-bismol, some pain killers and some cute band-aids for your kids ;)
Add a headlight, utility knife, fire starters, bic lighter, and you are ready to backpack my friend!
Some extras: Hand sanitizer, sunscreen, cut up sponge to wash dishes, deet if you got bugs, bear spray if you got bears, bandana if you wanna look cool and dry your sweat, towel if you got places to swim, gaiters if you got pebbles and stuff that sneak up your shoes and rain gear.