If you haven't done the two Green River trips (GRSP/Ruby - Mineral, Mineral - Spanish) yet, you might want to reconsider. We did the SJ with young kids in two tandem canoes, so yes, it can be done, but we did it after the Green trips. The Green is a more forgiving river for newbies, though it will still require you to have your skit together. Bugs will be worse on the Green. Mineral - Spanish is a nicer trip, and the Mineral road will be open end of this month.
An excellent absolute beginner canoe trip is Green River State Park to Mineral. The park is a very nice park, with showers, grass and a humungos boat ramp where you can take all day to organize things before you put in. Next day and 1/2 is Utah ugly, but after that the canyon is great. We used Moki Mac for shuttle, and Bob Quist picked us up exactly on time at Mineral, and left us off next to our van at GRSP. We had made reservations for a campsite before we left, so 15 minutes after we were back the tent was up and the wife/kids were headed for a shower. Moki Mac will also do the shuttle from Mineral back to Ruby if you want to avoid the first day of ugly-open.