Well, good luck. Neither my parents nor my wife's had any interest at all in even going vegetarian much less vegan. My folks at least don't fight the idea, though they are not particularly convinced of it's healthiness. My wife's family is dead set convinced we're all going to wither away and die even though we've been vegan for 4 years now and still here and healthy with two growing kids. Old thinking is hard to change.
That said, all major medical organizations have concluded that vegetarian diets are very healthy if not healthier than meat based diets and vegan diets are at the very least "adequate" if a little care is used. A little searching on the web should yield results you can show your mom. I seem to have misplaced the links I used to have to such articles or I'd post them for you. Otherwise, it looks to me that you're on the right track.
Oh, and one other thing, be prepared to accept the possibility that you may never get the support you are looking for from family. Some people are simply unwilling to look at the issue, for whatever reason. The key to maintaining a relationship with such people in my experience is lead by example, but don't push the issue. We had to drop all discussion of anything relating to animal welfare with both our families. They don't want to hear it and every time it got mentioned, even in passing, it resulted in bitterness and hostility. Now we're just the weird relatives that eat funny and still somehow manage to survive without any protein, but at least we can still come over for Christmas and they'll even go out of their way to make something vegan for us.
I hope it works out well for you, just be prepared.