I thought some relevant canons might help (there is a chapter in the code on parishes, pastors, and parochial vicars):
Can. 519 The pastor (parochus) is the proper pastor (pastor) of the parish entrusted to him, exercising the pastoral care of the community committed to him under the authority of the diocesan bishop in whose ministry of Christ he has been called to share, so that for that same community he carries out the functions of teaching, sanctifying, and governing, also with the cooperation of other presbyters or deacons and with the assistance of lay members of the Christian faithful, according to the norm of law.
Can. 545 §1. Whenever it is necessary or opportune in order to carry out the pastoral care of a parish fittingly, one or more parochial vicars can be associated with the pastor. As co-workers with the pastor and sharers in his solicitude, they are to offer service in the pastoral ministry by common counsel and effort with the pastor and under his authority.
§2. A parochial vicar can be assigned either to assist in exercising the entire pastoral ministry for the whole parish, a determined part of the parish, or a certain group of the Christian faithful of the parish, or even to assist in fulfilling a specific ministry in different parishes together.
Can. 548 §1. The obligations and rights of a parochial vicar, besides being defined in the canons of this chapter, diocesan statutes, and the letter of the diocesan bishop, are more specifically determined in the mandate of the pastor.
§2. Unless the letter of the diocesan bishop expressly provides otherwise, a parochial vicar is obliged to assist the pastor in the entire parochial ministry by reason of office, except for the application of the Mass for the people, and to substitute for the pastor if the situation arises according to the norm of law.
§3. A parochial vicar is to report to the pastor regularly concerning proposed and existing pastoral endeavors in such a way that the pastor and the vicar or vicars, through common efforts, are able to provide for the pastoral care of the parish for which they are together responsible.
The code is, as is often the case, somewhat vague about the specific relationship between pastor and vicar. Some things I thought noteworthy, though:
A vicar is “under the authority” of the pastor, yet the relationship sometimes seems to be portrayed as one of consultation in order to meet the needs of the flock.
A vicar is obliged to “assist” in all ministry, but the terms of this assistance are not spelled out.
Universal law envisions particular law and even particular appointments provided more details on the rights and obligations of both pastor and vicar - which means that we have no way of knowing with certainty what the exact situation in a hypothetical parish might be.
One last point: I think we can say that there are actually broad areas in which a bishop does not have the authority to demand certain practices. For instance, I would say he can’t demand that all his priests use exclusively Eucharist Prayer II, or option C for the penitential rite, etc. If a bishop (who has more general authority and liturgical authority in his diocese than a pastor) can’t do this, then it stands to follow that a pastor probably can’t either. Now, there are situations in which decisions can be made at lower levels, so we can’t exclude the possibility a priori, but it does seem smarter to err on the side of the pastor having less authority than the bishop.