Somewhere around the early 90s or so, maybe sooner, Notre Dame made the decision that it was no longer feasible to maintain its Independent status in all sports. It needed a conference to park all sports besides football. Initially, it went with the Big East because they were adding several teams like Miami, Boston College, and Pittsburgh in order to have football. But, in order to do that, Notre Dame had to make a deal and the deal was to give the Big East 3 of its football games each year. This worked out fine until the last round of expansion which decimated the Big East. So Notre Dame had to shop around again. I'd be curious just how close they came to making the decision to join a conference in all sports, because IMO, the ACC is the only league out there that would have been willing to take them on in a partial status. Of course, the ACC had more clout than the Big East did, so they got 5 Notre Dame football games each year.
Anyway, long story short, Notre Dame is where it is because they don't want to fully join a conference in football. The ACC was the only league out there that was willing to take them on in a partial status.
I still have no clue as to why Rutgers was invited to the Big Ten.