Yes and no. Each of the Sacraments has its own liturgical books, also funerals and RCIA etc… The entire collection of such liturgical books are in harmony with each other. One would never contradict the other (unless a more recent printing of one includes some recent changes) Something might be spelled out in the RCIA in more detail than in the Sacramentary for example.
The books complement each other. The Sacramentary says that the Gospel is read “here” but one needs to actually read the Gospel from the Lectionary.
The problem here in this thread is that people feel that they can rely on non-authoritative books or other non-authoritative sources to make changes to the Mass which the Church has not approved. That’s the problem. The people who print missalettes or who offer suggestions for changes to the Mass in magazines or newsletters are not the ones who have any authority to make changes to the Mass. This causes no end of confusion among Catholics. Many Catholics feel for example, that if a variation of the Lamb of God is printed in the Missalette, that means that it has been approved for use in the Mass. That’s simply not the case. The same holds true for ritual actions in the Mass. If it hasn’t been approved by the Church (and ultimately that means it needs the approval of the Holy See), or the Holy See has not specifically approved that something different may be said or done in a particular place, then doing so is never acceptable.
Just because something is commercially available, doesn’t mean that we can trust it. Take an example from the secular world. A person might buy a book on tax preparation. That book might offer some information which is not in harmony with the tax code. Such a person would not present the book to the IRS and say, in effect, this is the book that defines how I do my taxes, and I am at liberty to ignore the tax code because of it. You know what would happen in such a case. That’s what is happening with the Mass.
The real question here is “where is the second Alleluia described?” Omitting it from the Sacramentary or Lectionary would be a very unusaul thing for the Church to do if it is indeed approved. Perhaps it’s in the Pontifical because it applies only to a Mass celebrated by the bishop. I don’t know. But what I do know is that if such a thing were indeed allowed in a Mass celebrated by a parish priest, it’s safe to say that it would be included in the Sacramentary, GIRM, or Lectionary.