What came to my mind is... Why even give your new diet a name? You don't have to call it vegetarian. Just tell your parents you'd like to eat more vegetables for dinner. It's not disrespectful to cook your dinner. You can say hey mum, I want to learn to cook! Can I try this new recipe I found? Absolutely no need to mention veganism at all. And when your dad makes his BBQ? I guess you won't feel so bad about it because your meat consumption will be lower and your body will welcome a source of protein.
BTW not eating meat will not help you lose weight. On the contrary, too much carbs will make you hungry. I'm sorry I know this isn't the topic of this thread, just don't want you to make the same mistake I made in my younger years. Look up term "insulin swing".