Is the practice of the Elijah Cup or the traveling Cup for vocations, where the parishoner takes home the consecrated chalice used at Mass and prays for vocations at home, sanctioned by the Church?
I am unaware of any authoritative Vatican document establishing the practice, but it is something that a bishop could probably allow in his diocese. Of course, families who take home the consecrated chalice should be instructed in how to care for it properly, which would include not drinking from it in any kind of private devotional service such as an agape feast. A consecrated chalice is used to hold the precious blood of Christ and so can no longer be used for any lower purpose.
It would also be best for the promoters of this program to choose a different name for the program than “Elijah Cup.” An Elijah Cup originally was, and still is to this day, a traditional cup used in the Jewish seder at Passover. To co-opt this term for a Catholic vocational program seems somewhat disrespectful to the Jewish people for whom this tradition has had a very specific meaning and it could cause confusion.