I’m no nutritionalist, so I’ll let someone with a bit more knowledge answer that side of your post
However, I think your children have an equal chance of inheriting any genetic condition, regardless of what you eat Of course, what you eat during pregnancy can have other effects, and what you eat in the interim could potentially affect your fertility. But I haven’t heard of veganism causing a problem in either case, so long as you stick to a healthy balanced diet (and don’t just live off chips! ) There’s quite a lot of books around on the subject, looking at the vegan society [vegansociety.com]
I think seeing your dietician is a good idea, and it might be a good idea to take your parents with you. You could start with a quick, concise reason as to why you want to become vegan (try and write it down in a couple of sentences before you go?) Your dietician may not know a lot about veganism, so you could go armed with some facts: Why are eggs important in your diet (do you rely on them for protein, b-vitamins, fats, or other nutrients?) and how do you envisage gaining these nutrients if you become vegan? There are vegetal sources of these, but be aware that vegans are advised to take B12 supplements.
I have also heard rumours of people becoming wheat intolerant or allergic when becoming vegetarian (though I think it’s different to coeliac disease?). The only case I personally know of, was a girl who basically lived off pasta and toast, and was under a lot of stress too So I guess it’s understandable that your parents are worried. I ended up putting together an information pack for my mum (she was worried too!) full of leaflets, printouts from medical and sports nutrition websites, some recipes and a list of vegan foods. She said it meant a lot to her that I had done this research
A point worth remembering: if your family eat meals together, you are essentially asking your parents to do extra cooking, and buy extra foodstuffs (and probably supplements) which can be expensive or difficult to obtain in some areas. Now, I don’t know your personal circumstances, but offering to do some extra chores, cook some new dishes with your parents, or pay for supplements, may help smooth things over
I hope that helps a little… Good luck!