My daughter is a 17 year old junior in a private school. She's been there since she was in 1st grade. And even though we are in an area with some of the highest rated public schools in the Midwest, many chose this school for it's curriculum. They tend to teach 1-2 grade levels above the public system. So I get it. There is 'extreme' wealth in this school as well.
I also can understand coming from solid middle class values, although I would probably say, looking back now, we were low middle class. And somehow I remember thinking I need to stay true to my roots. My Midwestern, middle class roots. And as my husband always says, it's only a game if you choose to play.
I will admit that when we first put our kids (our son started when he was in 6th grade), in that school I never went in the doors unless I looked a certain way. If I wore jeans, I threw on a blazer and loafers. Now it's jeans, a denim jacket and my beirkenstocks! I'm still me. So you need to get ahold of your issues before they spill over to your daughter.
Growing up in the environment, sure there were differences in the parties etc. One of my best friends would through the most elaborate parties. But then the kids had just as much fun at my daughter's old fashioned skate party at a local rink.
Our son was a little older when he started there and there were comments made when some of his best friends started getting brand new cars when they started driving. You know what, we could afford a new car, but he didn't get one. And once we explained he was damn lucky just to be driving and not having mommy drop him off every day he shut up. AND THAT CAR is the car our daughter is now driving.
I can't say I did it on purpose, but again maybe changing my attitude about it all came through. One of my son's best friends (and they are still close now that they've been out for a few years) lives in one of the biggest homes and one of those families with multiple homes, one in Ireland! His mom and I are very close, I love that woman! Because SHE is down to earth. Her kids also did not get new cars. She cuts coupons and will be the first to point out how kids in our school are over indulged. So she too looks at things differently and that it's only a game if you play.
As far as applying for financial aid, if the school keeps their mouth shut, which they should, no one should know unless you tell them. Why does anyone have to know? I certainly don't know who is on scholarship and who isn't in our school.
I think you have nothing to apologize for. You are making a choice for your daughter because you feel it's the best choice with the information you have. You are very fortunate that you can offer her this opportunity. But what you need to do is get some help. Talk to someone about your issues with money and get a hold of that so they don't spill over to your daughter.
Blessings.