A few things concern me.
Firstly, how did your children decide they wanted to be vegan?
I understand that you have strong personal beliefs about eating animals but you've made this decision for them. I find it disturbing that they get no say in what food goes into their own body as they grow and develop.
We are omnivores with large and small intestines and canine and molar teeth to process our meat, fruit, grain and vegetable diet. Our bodies actually show us what we are supposed to be eating to remain healthy.
We are not evolved to eat highly processed additive filled and artificially flavoured food, and it sounds like your children are eating sausages and nuggets which are exactly this, vegan or not. Have you actually read the ingredients?
I was a vegan in my teens (though to be honest it was more akin to an eating disorder) and made myself extremely unhealthy by being so extreme in my diet.
I was also a huge campaigner for compassion in world farming but eventually came to realise that what I was advocating was genocide because some animals are only bred for food. If we don't eat them, their eggs, use their wool, drink their milk, then they will simply cease to exist. I rationalised that it is better to exist, live a healthy life with plenty of food and then have a quick death before illness or a predator strikes.
I do still care about animal welfare so only buy free range meat and eggs. This extends to eating out where, unless the pork/chicken dish is specified as free range, I'll go for the beef or lamb which is grass feed or the fish or vegetarian option if not certain.
I would never, under any circumstances, impose my beliefs on others, least of all my children and I'm not really surprised at your attitude that everyone must bend to what you perceive as superior beliefs to theirs.
I hope this post gives you some food for thought, even if you do just reply telling me how much unprocessed fruit, veg and grain you give your kids and how they just love vegan food.