[Ultra Sonic 007]

This is a bit of inside baseball knowledge, but a rather prominent example among Traditionalist circles is what happened to "The Nine" that got kicked out of the SSPX due to their disagreements with Abp. Lefebvre and the SSPX about the increasing accomodations with the Vatican as to the liturgy.

The Nine vs. Lefebvre: We Resist You to Your Face. Written in 2008, it serves as a recounting of the events by the late Fr. Cekada, which does include discussion of property and legal issues.

(A transcribed copy of the original letter, for reference.

[Alberta's Child]

In my experience, U.S. courts have little patience for internal religious disputes like this. At the end of the day, the only thing that will typically matter is who holds the title to the property, and (as in the case of Chicago, where the ICK holds the title) what legally binding agreements are in place between the diocese and the organization that owns the property.