We have a raft and a cataraft and an 8 year old boy who has been on the water since he was 18 mos old. We've taken him on both boats and his bopping around and/or random napping still makes me nervous on the cat. I prefer to take him on the raft, especially when the water is cold.
Duckies or inflatable kayaks might also be an option if you can find a fleet for sale or two tandems. You can paddle them upstream or down like a kayak, but they pack easily and require little instruction to use.
A 14' raft is a great start for a family of 4 for day runs or short overnights on the kind of water you are talking about.
Good luck and welcome! The best times we have are rafting as a family.
"There is NOTHING--absolute nothing--half so much worth doing as simply messing about in boats. Look here! If you've really nothing else on hand this morning, supposing we drop down the river together, and have a long day of it?" -Wind in the Willows