You have lots of questions on your plate about this - which is good. I'm going to seperate them out:
1. Her nutrition
2. Her visits with her Dad
3. Her visits with other members of the family
I've also put the above in level of importance.
Right now, she wants to become one. So, first off, work on her understanding of how she needs to eat. "Becoming Vegan" is really good for nutritional info the is easy to understand. And, it doesn't take a lot of brainpower to add cow milk for soy milk, and the occasional egg for tofu as necessary into her diet, if applicable.
I would advise taking things slow. As a child, she may jump into it head first without realizing what some of her favorite foods are. GIve her time to adjust. Let her choose some of the meals.
Once she is educated enough to make those decisions on her own, then worry about the father and the family. In the end, you cannot completely control non-illegal activity at a family member's house or at another parent's. You may have to wait until she herself stands up to them and insists on vegetarian food. There is nothing wrong with her being a veggie with mom and an omni with dad and grandma. There isn't anything wrong with that. I'm there right now - nothing wrong with it and no, the kids don't get confused.
If you have any questions about nutritional requirements, etc, just let me know and I can do some research for you.