My school had a set of twins rushing a few years ago. They were both deadset on another house that historically took all the girls from their hometown. They had both been really nice all week and we really did like them; one twin knew a lot of girls in our house through sports and the other one had been very polite but seemed a little disinterested and (as we found out later) had been saying very bluntly to the other houses that she was not interested in them because we were the only other house they would take if they didn't get their first choice house (gee thanks!) Because of this they had been dropped by everyone except us and their first choice so on pref night they both preffed us and the other house. Well I guess they ended up low on the bid list of the other house and they matched quota before they got to them so they had to go to their 2nd choice (us). Unfortunatly for the one who had been going around announcing that we would be her fallback if she didn't get the other house we had placed her low on our bid list too and we matched quota before we got to her but after we had placed the other and we couldn't take quota additions because we were already at campus total. So one twin ended up getting a bid from us and the other fell through completely. It was very tense for the first few days of whether or not the one twin would depledge and rush again for the other house with her twin the next year or if she would stay. Their parents were very unhelpful too, we got a letter from them basically telling us that they would force their daughter to depledge if we didn't offer her sister a snap bid. They also sent a letter to the other house demanding to know why they both hadn't gotten bids from them. Finally the director of greek life had to get involved and talk to their parents.
But in the end the twin that did get a bid started making friends with her pledge class and getting more involved in the chapter so she decided that she had made a mistake by not putting us first on her bid list to begin with and told her parents to back off. Ultimatly both twins decided that it might be better if they didn't do everything the same and even though they were still really close I think it was a relief to the twin in our house that she had other friends and could do things independently of her sister.
Her twin, who in all fairness matured A LOT during her freshman year, decided to rush the next year. We asked the twin in our house how she felt about her sister chosing us or another group and she told us that even though she would like it if her sister shared the love she had for our chapter she also didn't want to be "one of the twins" again and had liked having a seperate life. Her sister did attend our pref party but ended up pledging the other house that she had wanted the year before so I guess they both ended up happy!