"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.