Is your wife in agreement with transition to veganism for herself and for the children?
Here are some initial thoughts. Just somes suggestions here, not everything will work for you, pick and choose!
1. Take the time to do some background reading on ethical and environmental reasons for veganism, books, articles, movies, but also reading about recipe ideas, the more you do this, the more confident you are about the right decision for your family. Involve your family, e.g. Bite Size Vegan has some videos for children. Share books/articles with your wife, watch movies together and discuss.
2. Try some vegan variations of meat foods - e.g. soy/lentil burger instead of beef burger. You can have some of the same meals as before, just replacing the meat part.
3. But also be more creative. Instead of a plate of meat/soy+potatoes/rice/+ salad/vegetables, try mixing together peppers and vegetables with noodles, rice or pasta in a single dish. Involve your kids in the cooking process.
4. Make sure you get B12 (take as a supplement) and a source of calcium (a supplement, or calcium rich foods like almonds, oranges), iodine (if you use table salt, it may be added: check the ingredients) and omega 3s (flax or chia seeds or walnuts). Those are the nutrients that are most likely to be low on a vegan diet and needing of specific attention. If you want to, you can read more about vegan nutrition at
http://www.veganhealth.org/, a site with a good reputation.
5. Eat a general balanced diet including some legumes (beans, peas, lentils, soy), some filling carb foods (bread, rice, pasta), a variety of vegetables including some green vegetables, some fruit, a higher amount of whole plant foods, a smaller amount of junk and processed foods, and you are likely on a good path.
6. Vegan foods don't have to be unfilling like salad or just vegetables, so include legumes and/or grains at most meals, and remember some very simple foods like chips/fries or beans on toast can also be vegan.
https://www.vegansociety.com/go-vegan/how-go-vegan
http://features.peta.org/how-to-go-vegan/