I've spelled this out on other sites previously, but if Notre Dame joins a conference fully it won't be the B1G, it will be the ACC. The reason is that they are a religiously affiliated school, and there are NO other schools in the B1G that are. The ACC conversely consists of several other schools who are: Boston College (which is another Jesuit school like ND), Duke, Wake Forest, SMU and Stanford offers PHD's and lower degrees in religion and divinity.
The reason that this is important to these schools is that they need to feel that their choices of religion are not going to simply be out-voted by secular schools.
It is simply never going to happen that ND will join the B1G for that reason alone.