As for my parents, i have no idea what my fathers stance on LGBT is. I'm a little confused on my mother because i have heard her drop "fag" one or two times (never directed as an insult though) However she is in-humanly obsessed with Caitlyn Jenner and the show "I Am Cait" in a good way.
A couple things to realize. Some people oppose homosexuality on moral grounds. All those people are religious, the vast majority are older, and they're more concentrated in rural parts of the country. Others oppose homosexuality because it goes against their gut feeling. It just seems wrong, but maybe they can't put it to words. If your mother is ok watching Jenner on TV, she falls into neither of these categories. She's at least apathetically pro-gay. Your father might have a problem with homosexuality, but seeing as how you live in NYC, he also must feel immense pressure from the larger culture to keep his mouth shut. You might be met with silence from him, but I wouldn't expect him to protest.
Oldest brother no clue either but pretty sure he wouldn't give a fuck either way, My other brother is a "jock type" and obsessed with sports he says fag quite alot actually and in an insulting manor however i've never seen him outright attack someone for being gay. His girlfriend is 110% LGBT Alliance they've been together for a while now so shes basically like family.
Again, probably tacitly pro-gay. Statistically, at least 85% of 20 somethings are pro-gay marriage, and that's nationwide. Your jock brother might feel like gay sex is weird, but he's also been raised by a culture that thinks that view is bigoted.
I'm just not sure if this would be the best way to go about it, i don't want to ruin our vacation or anything but really would like to kill as many bird with one stone. lol ...
You're not telling your family you have stage 4 cancer, but it's not like giving them a Christmas present either. Even the most pro-gay liberal parents have to work through a lot of conflicting emotions when their children come out. Respect that you and your family are on vacation. You both want to kick back and enjoy yourselves and not have to think about the next hurdle life will throw at you. It's harder, but I would say wait and come out separately to you parents and siblings. Tell you parents casually at dinner one night, but wait until they're both in a good place and ready to hear it. Your siblings will find out from your parents, or you can tell them yourself.
Also i would like to add that im out to some, if not most of my friends and they're all very supporting about it. Surprisingly so since i go to a Catholic School, fortunately enough i live in NYC so more or less most people are okay with it.
Nothing surprising here. Catholics are actually statistically more likely to support gay marriage than the average American. This is even truer in New York. I taught at an all boys Catholic school in the deep South, and even there, I would say at least 75% of the guys were pro-LGBT by time they got to college.