Okay, I'll do what I can to give you accurate info without going into private membership selection. I've logged in to the DDD site and am looking at a reference form so feel free to ask a question. If I can't answer it for confidentiality reasons, I'll just say so.
A few other comments...
Tri Delta HIGHLY values legacies, but we also have more coming through than we can extend bids to on many campuses. I pulled out an old pledge manual I have from the late seventies (before my time!) and it says only daughters and sisters are legacies in the definition area. So that has been the policy for some time. Step-sisters and step-mothers may also be included in that according to the reference form.
I would suspect that any chapter that had a potential fourth or fifth generation Tri Delta coming through recruitment would give her an extra long look and consideration. Now I'm not in the room during membership selection and I don't know what goes on at every school. But it is enough out of the ordinary that I would be surprised if you didn't get more than a regular second look. If you are going through recruitment in the north, I would think this would definitely be the case.
I feel like I can't publicly address your sister's situation without getting into private membership selection.
You don't need a reference form from every Tri Delta you know. As long as one official form is submitted, that is all you need. All of the other Tri Deltas can submit letters of recommendation or letters of introduction.
I hope that helps! Let me know if you have a more specific question!
ETA: It is Tri Delta not tri-delt.