For most sororities, legacies are invited to first invitational round and, for many, if the legacy is invited to pref and she puts that sorority first, she will receive a bid. So the cut, if it comes, has to be after the first invitational and before pref. Also, several sororites, founded in the SEC area, have more legacies than openings and, since they leave some openings for non-legacies, legacies will be cut. Few girls are deliberately cut other than for grades and that usually happens after first round (or second if a legacy). Most remain on a list but are not near enough to the top to fit into the quota for the next party or bid.

The main problem here is that it sounds like your daughter went through recruitment with blinders on, set on pledging her legacy chapter. I wonder, does she want to be Greek, or is she only interested in her legacy chapter? I won't make assumptions about her thinking she was too good for certain chapters, though that is possible, but it just sounds like she was so set on one chapter, and that is a recipe for disaster at ANY school.
Sophomore status: Often a disadvantage. Alabama has a separate upperclass quota, but not all chapters choose to take upperclass members.
Very high GPA: Not sure how sophomore's GPAs are compared to freshman GPAs at this school--for example, a 3.5 in college is an excellent GPA, but 3.5 out of high school is just eh. If there is no separation in GPAs, her "very high GPA" might not have actually given her an advantage. (I am of the opinion that HS and college GPAs need to be evaulated separately, but from what I gather, it is not always the case.)
Very beautiful: so is everyone else...
Rec: Helpful, but more or less a foot in the door. Won't mean much if a PNM doesn't have other things the chapter is looking for. Remember, recs are for informational purposes.
Legacy status: In the SEC, there are tons of legacies going through. At some schools, some chapters could fill entire pledge classes with legacies and still have to cut some based on quota. It really doesn't mean much, and you can hope that your sorority followed its legacy policy. Does "dropped 3rd round" mean before or after 3rd round? I can't speak for every sorority, but generally if a chapter is going to cut a legacy, they like to do it before the 3rd round so the PNM has time to focus on her realistic options.

What we don't know is what kind of campus involvement she had in her first year, how many friends she had in this chapter, and most importantly, how her conversations went during recruitment. Also, why did she not go through as a freshman? Being a legacy at an SEC school, she is no stranger to Greek life. Why did she wait? Or did she go through as a freshman?
COB is only for sororities who have vacancies in total (the maximum chapter size as determined by the Campus Panhellenic). If a chapter is above total, they can not take any more members until next formal recruitment (or next semester, if they have enough women graduate in December to put them under total). If your daughter goes to Auburn or Alabama, all chapters made quota (their equal slice of the "pie" or PNM pool). That doesn't mean all chapters will be at or above total, but it is less likely there will be vacancies. It is entirely possible that NO chapters will be participating in COB. As for being a sophomore with COB, it is no more of a help or hinderance than it is with formal recruitment.

Different chapters conduct COB differently. Some will have open parties for any interested women. Some will invite women registered with Panhellenic. Some will quietly ask friends of members to join.
Yes, and yes. Those are both bad ideas that would bring her negative attention. Even if it worked, do you really think that your daughter would want to be known as the legacy whose mom paid for her bid? What kind of sisterhood is that?

I'm sorry it didn't work out for your daughter. She needs to evaluate if she wants to be Greek or if she just wants to be in her legacy chapter. Is her legacy chapter a "popular" one? You know, one that a lot of PNMs seem to want? It's possible that she has no chance of joining her legacy chapter but still may have the opportunity to be Greek.