Unfortuantely, there's a lot of families that aren't very supportive of someone going veg. Especially if that veg is underage, underweight or has had problems with eating disorders (not to say you have, specifically it's just that those tend to be the top 3 reasons among people that have had no familial support). And then there's the whole "meat wasn't a problem to you before and why is it suddenly a big deal now" issue..... some families are just resistant to change and really have a problem when someone in their set does. There's loads of threads round here dealing with that very same thing if you want to read how so not alone you really are. There's also a lot of good survival info in there as well so definately check those threads out, k?
For the household products, there might not be much you can do at all. Unfortuantely a lot of CF (cruelty free) products are also pretty pricey... almost too pricey for a lot of people's budgets. If you have your own money you might be able to buy some CF items for yourself but seriously, don't expect the family to change over straight away.... not unless you're buying their household products that is.
In the food front: center your diet around fruits, veggies, whole grains, nuts/seeds and beans/legumes.... you know, the stuff they're probably buying anyway. Special things like veg burgers and soymilk can be pricey as well and a lot of parents are really hesitant about laying down that sort of money on a regular basis. If you have a job/your own money, then it might be easier to buy those products but if not, you'll have to work within what your parents DO buy and do the best you can with that. Also, read everything you can about how to have a healthy diet so you're not running yourself into deficiencies. Nothing's worse than going veg then having to go back to being a meater because the health started screwing up (and believe me, if you ever want to give your parents good ammo on why someone should NOT be veg, developing bad health is definately the way to do it
I'd write more, but my puter is acting up. Welcome to VB
and stick around. The people here are good with support and question answering and often have no trouble helping someone out when needed.