That actually sounds pretty impressive. I agree with ST.

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Glad things worked out for you 
Hope you took some good pics to post, maybe one with the canoe loaded?
Others might benefit from your first-hand experience.

I started this post.  We just got back from our trip, which was just plain excellent.  We went with a Souris River 18.5 three-seater.  Me in the stern, wife in the bow.  2 packs in the open compartment behind the bow - one of which was a softer pack with clothes, sleeping bags, etc.  6-yr old sat on top of the soft pack.  8 and 10 year old shared the 3rd seat.  The 8 year old sat backwards on the seat, 10 year old sat forward and paddled.  That allowed me to put another good side pack just in front of the 3rd seat but only taking up half of the space.  Total of 5 people, 3 big packs and 2 small backpacks for the trip, plus  fishing rods.  Tight fit but we made it comfortably and were able to move at around 3 mph on the water. 

Bohnsack, I think you're on target with the MN4.  If this is the way you have to go to make it work, it beats not going.  You can plan your route to take advantage of the big boat's strengths, ride out the weather if too windy and stick closer to shore to avoid getting caught in the open.  The MN4 has large flat center seats (if renting, double check with your outfitter for the seating layout). Most outfitters will have at least one.  I'd go with mom up front, 10 year old next, the younger ones side by side third seat, you in the stern.  If that doesn't work out, you could put one center sitting on a pack.  Ditto what MM said about mom and front steering strokes.  You should easily be able to fit 5-6 large packs in there too.  Smaller packs work better so the younger ones can be more help on portages.  If fishing is in the cards and it's less than calm, throw a few packs in sitting low to help stability and lower the profile a bit.  Good luck with the planning.

pd

I was thinking more in terms of getting caught with the winds coming at you from the side and trying to turn the bow into the wind?

  I guess it depends on a lot on the skill of stern paddler and how much help the other paddlers can give.
From the original post, it doesn't sound like that's a sure thing?

Momentum is a great thing when it's working IN your favor not against it.

"I can't imagine trying to maneuver a heavily loaded barge like that without 2 STRONG paddlers minimum.
You get caught with weather change in open water with only ONE strong stern paddler, I can't imagine things going well for you."

I agree to a point, but not totally with this.  When I used to work as a canoe guide, I occasionally was in the stern of a 24' Voyaguer canoe - usually had 3 or 4 other people (novice paddlers) and maybe a ton of gear - boat was 5' wide at center and weighed about 400lbs empty.  Once you got that mass moving, momentum worked in your favor and in strong headwinds it would outperform tandems easily - the same wind blowing a light and heavy weight will have more effect on a smaller mass - visualize a golf ball and a ping pong ball set in front of a fan - which one do you think will get blown the farthest?  Building up and maintaining momentum is the key.
Paddling a MN 4 with the o.p's family, I'd have the two older kids paddling on the same side as mom, and definitely "trained' to paddle in sync with mom, stroke for stroke which should offset a strong stern paddler. and have mom learn a bow draw and sweep to help steer that big boat from the bow.

Quote:

Or winds other than head/tail 
I can't imagine trying to maneuver a heavily loaded barge like that without 2 STRONG paddlers minimum.
You get caught with weather change in open water with only ONE strong stern paddler, I can't imagine things going well for you.

This looks like a fun way to go with a family.  Just no creeks!

Here is a photo of a large family and lots of gear in a big canoe.  They helped us in Aug 2015 when we had an injured member of our party.  As you can see it is a huge load but they seemed stable enough in the water.  I think the thing which would make you most uncomfortable is if your load is too much for the canoe so I would go huge.

I have done such a trip (only with 4 boys) and rented a MN 4.  It is a barge but is sufficient to the task of travel.  It weather-veins and it can be difficult to keep it on track in the wind but I had a 15yr old in the bow.  It's impossible to fish out of when it is empty.  So, if you're just traveling and hauling gear from place to place I think you will find it sufficient.  Can the 10 year old kayak alongside maybe?