Take a Kid Fishing
Fishing is a sport that everyone can enjoy. Most people will decide whether they like fishing or not as a young child. If the experience is positive, they will most likely enjoy it (and vice-versa). Fishing can be a dirty sport or a clean sport, depending on how it is done. You can fish out of a boat with artificial lures and wear your best clothing and go straight to church afterwards. Likewise, you can walk a muddy creek and use stink bait to catch some slimy catfish. Then you get yourself, your truck, your home, and everything else filthy. Some kids will love it, but there is usually someone in the family who won't. I recommend taking children out in a boat with someone who knows how and where to catch the fish. If you go with a guide and catch lots of fish, the kid will remember it and may decide to get into fishing instead of trouble when he/she gets older.
I am a guide on Lake Fork, which is about 1 1/2 hours from Dallas. I recommend a 1/2 day for young children or a full day for older children. I normally charge $100 extra for a 3rd person, but will take an adult and 2 small children for the price of a normal trip.
If you are interested in booking a trip on Lake Fork with small children, I recommend October and early November. That is the time we get the best numbers of black, white, and yellow bass. May thru September are often good months as well, but not quite as consistently.