I'd ensure you got professional advice before committing your children to a vegan diet. Personally, I have seen the article above before, and some others, indicating it's hard to ensure a child can get an adequate enough supply of nutrients to maintain healthy growth.
My wife was a vegetarian and we made a conscious decision our kids would not be, and that once they understood why my wife was a vegetarian, they could make their own minds up.
I have found articles outlining that sometimes, with a growing child, it is hard for them to maintain a good enough vegan diet due to the sheer weight, amount, of food they have to eat in order to maintain healthy growth.
I am not trying to be too overly moralistic here, but as with religion and other choices in life, please ensure you're doing this for the children, and not for yourself.
Anecdotally, I grew up with a vegan boy at school and he was forever ill, as was his curiously vegan dog.
Any potential risks of vegetarianism seem to be related to the type of vegetarian diet, i.e. the foods that are excluded. Vegan diets are more likely to be associated with malnutrition, whereas children eating a lacto-ovo-vegetarian diet consume diets closer to recommendations than children whose diets include meat. Their pre-pubertal growth is at least as good as children consuming meat. In general, the greater the degree of dietary restriction, the greater the risk of nutritional deficiency."