While I think Jamie Stringer may be rather dream-crushingly blunt, I have to mostly agree with her statements. The first admission gate is the GPA/LSAT matrix, and to the best of my knowledge it is applied pretty mechanically without any regard to undergraduate institution. Only applicants in the good part of the matrix get looked at by a person. A 3.5 GPA will be at or below the outright cutoffs for many of the top schools, regardless of LSAT, and that makes everything else irrelevant.
That said, my understanding is that the top schools have a gray area, where applicants with some characteristics (such as borderline GPA and high LSAT) get a subjective review, even if their stats otherwise would not qulify.
If OP makes it to the subjective review stage, then other things come into play, including the higher second-attempt GPA. As I indicated in my earlier post, I believe Yale (and some of the other top schools) might give OP a second look, but emphasis on MIGHT. And even then, admission is (IMO) unlikely. I am just more optimistic than Jamie, and encourage people to apply - just in case.
Does undergraduate institution matter? Yes and no. The GPA is the GPA. Once in the subjective review, schools might conceivably give preference to applicants from the very best schools over equivalent applicants from the very worst schools, but it would have to be an extreme situtation - and those are by definition rare. I expect that undergraduate school comes in to play more often as a diversity play - law schools might give preference to applicants from underrepresented geographic areas or underrepresented schools. And, of course, the anti-diversity - law schools might give preference to applicants from their own universities.
Short version: OP is unlikely to get in to YHS (the correct order), but just might, and should certainly try. Same for other top schools, although admission becomes decreasingly unlikely, of course.
Also - I am amused/befuddled by the acronym lingo. Can somebody translate for me? I got YHS figured out, but CCN? MVP? CLS? URM?