I agree that it is concerning that she wants to have the kids be vegan - it can be really, really quite hard for kids to get the protein and iron they need from a vegan diet. Even most ADULTS would have a hard time eating the large volume of spinach that would equate to the amount of iron available in just a small amount of meat.
I don't see why she isn't willing to compromise with your great-sounding idea of exposing the kids to vegan and omnivore diet - e.g. having vegan meals sometimes and having meals with meat in them other times. I do feel it is unfair when people push a 'restrictive' diet onto kids (who don't really get a say in the matter).
Would it be possible for you and her to see either a pediatrician (to get a qualified medical opinion for the kids) or go to a nutritional counsellor? Her issue may be a 'quantification' issue where she honestly doesn't realize exactly HOW MUCH beans, spinach, etc someone would have to eat to get enough protein and iron in their day. There are a lot of vegans and vegetarians who don't bother looking at exactly how *much* of certain foods are required to have a balanced diet. Many vegans think, oh spinach has iron in it, beans and peas have protein. But they don't look at HOW MUCH they would need to eat of it... they just think that if they eat a bit of spinach and a bit of beans they are OK. That is not true. So try asking her to calculate out how much of what types of foods she would need the kids to eat.... she may realize how hard it really is to have a balanced vegan diet, espcially for kids!
As an example of this approach, my sister had low iron and was trying to increase it (while on a vegetarian diet). I suggested she look at how MUCH iron she was taking in on her diet, by comparing how much % daily iron values on the nutritional info of stuff she was eating (on most food labels, or you can find it on the web for fruits & veges). I said that ideally she would want a diet that gives her 100% daily iron values, or ideally be above 100% if she wants to increase her iron levels. She thought that was a good idea, and calculated how much iron she was actually getting. A few months later, I called up to ask how she was doing. She told me she actually went back to being an omnivore after realizing how hard it was to get enough iron on her vegetarian diet!