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Every Catholic who is not a Bishop is under the authority of a Bishop, and if the Bishop is not the Pope, the Pope as well. The Pope, or those delegated by him, determines who is under what Bishop, normally by determining the boundaries of dioceses and by appointing the Bishop of the various dioceses.

Some groups of religious (nuns, monks and the like) are what are called exempt: the Pope has exempted them from the governance of the local Bishop. This exemption does not extend to actions that affect those outside of the exempt group. Some religious are not exempt.

The relevant doctrinal passage out of the Vatican II Document Lumen Gentium (known in English as the Dogmatic Constitution on the Church) reads as follows:
"With a view to providing better for the needs of the whole of the Lord's flock and for the sake of the general good, the Pope, as primate over the entire Church, can exempt any institute of Christian perfection and its individual members from the jurisdiction of local ordinaries [i.e. bishops of dioceses] and subject them to himself alone. Similarly they can be left or entrusted to the care of the appropriate patriarchal authorities. Members of these institutes, however, in fulfilling the duty towards the Church inherent in their particular form of life [e.g. teaching in the case of the Lorettos] must show respect and obedience towards bishops in accordance with canon law, both because these exercise pastoral authority in their individual churches and because this is necessary for unity and harmony in the carrying out of apostolic work." (LG 45--Flannery translation, 1988 edition)

The appropriate section of Canon law is canon 678, which reads as follows:
Section 1. Religious are subject to the authority of bishops, whom they are obliged to follow with devoted humility and respect, in those matters which involve the care of souls, the public exercise of divine worship and other works of the apostolate [e.g. running a high school in this case].
Section 2. In exercising an external apostolate [e.g. running a high school], religious are also subject to their own superiors and must remain faithful to the discipline of the institute which obligation bishops themselves should not fail to insist upon in cases which warrant it.
Section 3 In organizing the works of the apostolate of religious, it is necessary that diocesan bishops and religious superiors proceed after consultation with each other.

The situation is thus undoubtedly complex. The high school is an external apostolate, so, given section 1 of canon 678, it ought to be subject to the bishop--and thus the bishop could be justified in demanding the dismissal of the high school teacher. Identical justification could be used to intervene with regards to the expulsion.

The trick, in my estimation of Church politics, is in sections 2 and 3 of canon 678--if the provincial superior, who is outside of Sacramento, and thus outside of the Bishop's jurisdiction, has already implemented a discipline contrary to what the bishop would like to see done before the bishop intervenes, further action can take place only after the bishop and the superior come to agreement. Thus, the one who makes the first move wins until they decide to compromise until and unless Rome intervenes.

Frankly, from what I have experienced and heard of the Lorettos (my wife is an alumna of a Loretto High School), as they presently exist, the Church would be better off without them.

Traditionally, there are three ways of getting rid of exempt institutes.

One is to suppress them: the Templars (1303 or 1305--forget which) and the Jesuits (who were suppressed in 1773 and revived in the 19th century)being the most famous examples. This method is normally resorted to only in extreme circumstances, which, in the Church's perspective, translates into once every few centuries. Historically, the process is usually traumatic.

The second is to forbid them to receive new members. Franciscans are always fragmenting. Various Popes have attempted to bring more unity to the Franciscans by forbidding the reception of novices by any community of Franciscans unwilling to join with one of certain designated groups. This would be redundant in this particular case, because the IBVMs, at least on this continent undoubtedly have virtually no novices. One would merely be ticking off a bunch of battle-axes for no good reason.

The third is to let nature (or rather providence) take her course. The Lorettos, and a great many other orders, are presently Dead Men Walking. Forty years from now, their main presence in the Church will be found in Catholic cemeteries (maybe sooner depending on how quickly euthanasia catches on).