Roof Top
I had the same problem for years. I purchased some good heavy duty water resistant duffel bags and put them directly on the roof, under the canoe. You may have to remove the yoke. You can also get a long narrow roof box, but you will have to also get longer bars to fit the canoe next to it. Do invest in a set of good food racks to carry the canoe long distances at hightway speed.
Hitch?
I like the idea of the big bags secured to the roof under the boat. I gotta say though, with two little ones that young (God bless you for even considering this trip LOL!) that plus any other space you have might not do it. Do you have a hitch? If so maybe you could also employ a cargo basket. Those things are the cats. You might even consider renting a small trailer from Uhaul (think someone mentioned that already). Uhaul trailers are one of the best equipment rental values going IMO. It would have to be really small of course, and again, this is predicated on the assumption you have a hitch.