I know this may be a little late considering recruitment ended almost two months ago, but I know that getting over something like this can be difficult, so I hope this can still help.
Recruitment can be really hard. Everyone is under a lot of pressure--pressure to look good, be charming, be the whole package...while standing outside all day and walking from house to house in the brutal heat while wearing heels. At the same time, it can be one of the most wonderful experiences in the world. I had a horrible experience last year going through recruitment, but I went through again this year and everything worked out amazingly. I'm not sure if your daughter would be interested in going through recruitment again, but I hope my story can help.
I was so excited to go through recruitment last year. It seemed like the whole week was going amazingly--I got invited back to all of my top choices every single day--even on pref day. But on Bid Day, right while I was getting ready, my Pi Chi (recruitment counselor) called me crying to tell me that I was not receiving a bid that day. She said that she was shocked because it seemed like I was a shoo-in--the typical sorority girl. I knew what had happened--I preffed 2 sororities on pref day--we'll call them XYZ and YX. I really felt a strong connection with YX but I felt like I had to go XYZ because of what the girls in my pi chi group were saying and because of their overall reputation nationally (at least from what I heard at that point). When the girl that preffed me at YX asked if I was torn or not, I honestly said yes--that I loved them both but just didn't know yet. She later told me she thought that I wanted XYZ much more and that she could just tell and she told the other girls that, so I didn't end up on their bid list. Everyone assumed I'd be getting a bid from XYZ, especially a good friend of mine in XYZ. As it turns out, they dropped me on Bid Day. To this day, I don't know why. Sometimes, you never do.
Your daughter is probably as beautiful, intelligent and incredible as you say. I thought I was the whole package,too--not in a conceited way at all, but I thought I had a lot to offer. As it turns out, I did. I can't even begin to tell you how painful and crushing it feels to be turned down and watch all your friends so excited, waving around their bid cards...especially when you were the one that was going through recruitment for all the right reasons--for the sisterhood, the memories, the true college experience I had always dreamed of...not just to wear the letters or meet fraternity guys, like so many girls I knew going through. Ironically enough, XYZ ended up extending bids to girls that never came around or dropped the sorority, etc.
I know realize, though, why I didn't get a bid from XYZ--or YX for that matter. It wasn't meant to be.
I think everything happens for a reason...and I later found out that reason was that I belonged somewhere else. Somehow, on that first day of recruitment last year, I overlooked the house where I belonged. Luckily, I mustered up all the strength I had to go back through recruitment again this year and I found that home. It is the sorority that I am in now and it is the most incredible thing in the world. I've found girls--sisters--that I love to be around, that never pass unncessary judgement, that are there for me if I want to laugh, cry, study, go out or stay in. I can't imagine life without my sorority now. I've only been in it for a little under two months but they have been the best two months of my life. I remember on Pref Day when of the girls broke down crying as she talked about our sisterhood and how amazing it is. Today, that is honestly, 100% how I feel. I feel like last year was a learning experience--a painful one--that I needed to have to teach me to appreciate what I have now.
I wish that your daughter got to experience the amazing things that sorority life has to offer. I will never forget Bid Day this year...I cried, once again, but this time it was because I was so HAPPY. All the girls gather in the quad in Greek Village and they shout "Go home!" and we go running to our houses. Seeing all those girls smiling and crying and welcoming you in is the most amazing feeling in the world and it more than makes up for how awful things were last year. I hope that your daughter gets a chance to experience this.
I know went she went through was awful and right now, neither of you can probably imagine going through that all over again, but I promise you-it is worth it. I can't promise that she'll get a bid this time around, but there was this quote on Grey's Anatomy, and I realize this is cheesy, but it really represents this situation to me...it says "...even the biggest failure, even the worst, beats the hell out of never trying" and I think this really rings true for greek life and the recruitment process. It was 100% worth it.
I'm not sure how UGA's system works, but I do know that we have to rank everyday. Maybe the way your daughter ranked the sororities didn't match up with the way they ranked her. I can't swear by this, but I am fairly sure that there was at least one sorority out of those 18 that wanted her and that would have been a perfect fit.
I know you can't go back to all the houses in round 2, so you need to rank after round 1 (this is usually how it is)--in that case, something like that may have happened.
Even though I went through again and everything just clicked, I realize that your daughter may completely oppose going through again and I can definitely understand that. In that case, it's important for her to realize that she has family and friends that can make her just as happy as any sorority can. She can get involved in clubs that give her a sense of belonging and make a huge, overwhelming school like UGA much smaller. She can always go to fraternity parties and different Greek philanthropies and events with her sorority friends just to see what it's like or experience some of the things she wouldn't ordinarily get to. I spent 2 years in college not being in a sorority and though for me sorority life is a million times more amazing that those past 2 years, I can honestly say I still managed to have the time of my life back then. I made great friends in my dorms that I still keep in touch with. I joined a few different clubs and spent a lot of time on my schoolwork. I went to every single college event and got involved as I possibly could and I loved every minute of it. Yeah, I thought about going Greek and what I was missing out on a lot, but you know what? I had fun. These four years are about discovering yourself. And maybe your daughter discovered she doesn't need a sorority to be her wonderful self. Being Greek is an incredible experience, but college in ITSELF is an incredible experience. Whether she gives Greek life another shot or goes down her own path, she will eventually get over this and everything will fall into place.

[P.S. I'm not sure if UGA has spring rush, but it is usually much more informal and laidback. You usually just visit one house at a time to decide where you fit in. If she isn't offered a bid, she can go to a different sorority's spring rush party and see how it goes there. There usually isn't a "Bid Day" or anything like that. My school has this, so UGA might, too.

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Sorry this was so long, but I hope it helped. Even if not, please tell your daughter that college is what you make of it and if she wants to have the time of her life up there, she will.

Good luck to her in college!