Texas paddle trails are fun! If you are canoeing, I'd suggest a practice run at a flat, still lake, or maybe even a day long workshop. When we started paddling, a workshop is fun and we learned a couple years skills in a day. A great family outing and will save you a ton of frustration.
When paddling with kids, you'll be doing 90% of the work. They get tired and distracted, you'll be the pack mule. Find flatwater (lake), low wind. Pack a lunch, have a picnic. Fish.
Many of our Texas state parks have canoe rentals on their small lakes and are perfect for adults/kids to learn.
I would NOT start out on a river...unless it's flat and still....until you paddle with your kiddo and get used to each other in a boat. Like I mentioned, you'll be doing most of the work and fighting currents, wind, and tired kids will exhaust you pretty quick, especially with no training. You have gobs of paddling options around your part of the state. Check TPWD, Boy Scouts, YMCA, canoe/kayak dealers for workshops. Paddling is a life long sport your family will really enjoy!