First of all, that's a dangerous thing for them to do -- lactose intolerance starts building up when you don't consume dairy for a long time -- I once got violently ill from a similar experience.

Second, simple vegan potato recipe (my go-to for at least 1 meal a day): Poke a bunch of holes in a potato and microwave it (the way you'd normally microwave-bake a potato). Cut it in half, add some vegan margarine and some salsa. Then, sprinkle the top with whatever topping you prefer -- I prefer something salty like Daiya or some kind of vegan dairy alternative, however other condiments will work (it's kind of like a potato pizza). Then, microwave it to heat the toppings on tip and you're done. Maybe a 10 minutes-to-prepare meal. If you don't feel you can trust them, maybe don't buy vegan dairy alternatives and stick to other stuff?

When you attend university, you'll have to be self-sufficient, so these quick recipes can be absolutely perfect. As far as home-living is concerned, I wouldn't expect your parents to adopt the same diet as yourself. Usually by that point in their life they're pretty set in their ways and won't want to prepare 2 separate meals each dinner time. It would probably be best to explain your position -- why you want to be vegan, why you don't think it's necessary to consume meat, and possibly make compromises (like regular nutrient level checks). In my experience though, it's almost always necessary to make your own meals, and sometimes it can be helpful to work on preparing a fully vegan meal together (like one of those huge recipes that need 2 people to coordinate)

I think I read in one of your comments about religion being a point of argument. The Bite-Size Vegan did a bunch of youtube videos detailing the history of veganism and in one of them she mentions how originally the most righteous people in the christian religion could not consume meat. That rule has only been relaxed in the past few hundred years (apparently it's more convenient to ignore certain parts of religious scripture)

Anyway, that's some food for thought