wow. I hope we will all be nice.
I was in the same boat in the 80s. My mom was convinced I'd die without eggs. In reality, people around my digestive system want to die if I eat eggs, but I digress.
You'll see that some people perceive L/O as a passage to being vegan, or a cop out, or worse, but reality of the veg world is lactos are huge, and out of India, the same goes for ovos (and l/o of course).
It's YOUR journey, not anyone else's, and do what resonates in your soul, fills your heart and rests easy in your intellect.
it helps to know why you are veg, how you intend to meet all nutritive needs, and cooking many dishes on your own really helps!
I was cooking for myself by 80-81, so aside from the dreaded bbq weekends when mom and step dad were around, it was almost unnoticed!
oddly, it was my former and on-again-off again veg step mom who slipped meat and broths into food.
how weird, eh? Still don't get it...maybe she felt my going veg was an indictment of her return to omni, but I learned that starting all answers with "for me..." made far less arguments.
Peace is good, especially in your homes.
since your parents are veg, you have a great foundation, and probably less hassle that the child of at least one omni.
look in their cookbooks and other books: why are they in the "must" have eggs/cheese camp? what do the texts they own tell them?
I know that it is seen as easier, but it is also "cholesterol salad."
Perhaps making eggs and cheese so low in your consumption that they easily fall away can help.
Do your parents make a lot of egg/dairy based dishes?
I've yet to find a vegan cheese sub that is worth the effort and money.