The short answer to your question is that theological justification for believing in the real presence of Mary in the Eucharist would be by the same means that believing in pray to Mary and all the attributes (dispenser of all graces, power over all the angels, etc.) are justified, which is by extrapolation. Based upon the premise that Mary "never left the side of Christ," then it is reasoned that she is present in the Eucharist with Christ, kneeling beside him. (http://www.wrldrels.org/articles/palmarian%20catholic%20church/palmarian%20catholic%20church..pdf)
The longer answer, and which tell more of the Palmarian sect, is that technically the tiny Palmarian sect is debatably not sedevacantist, since unlike them they accept the validity of Popes John 23 and Paul 6, and have their own popes, starting with Gregory XVII, who later admitted to sexual impropriety involving nuns (George D. Chryssides, "Historical Dictionary of New Religious Movements," p. 268) and left the church, and living with his girl friend, said that due to investigation he came to the conclusion that the Palmarian church was a set - up or a scam. (magnuslundbergblog.files.wordpress.com/2016/07/the-papacy-of-gregory-xviii-final.pdf)
Which relates to your question, as the extensive researcher/author ("Fighting the Modern with the Virgin Mary) Magnus Lundberg states concerning access to texts in general,
"because of the increasingly closed nature of the church, it is not easy to get access to the texts and very little is found in research libraries. They have to be acquired in other, sometimes, complicated ways." (magnuslundberg.net/category/palmarian-catholic-church/page/3)
And rather than being a group that is based upon the weight of Scripture and tradition, they began as an Apparition group and get their marching orders and distinctive theology from this Mary. Which does not mean what their adulation and they attributions they give to their Mary is far removed from what is seen uncensored in historical Catholicism, in which are found statements such as that Mary is an almost almighty being, to whom Jesus owes His Precious Blood to, with the Eucharist being "bread produced by Mary from the flour of Her immaculate flesh, kneaded into dough with her virginal milk.” (catholictradition.org/Mary/virgin-eucharist.htm)
However, Palmarian Church even went beyond this. Lundberg finds,
Within weeks of its foundation in 1978 , the Palmarian Church would develop this body of articles of faith at a rapid pace. For t hem , the Virgin has come to have an almost e qual status with that of Christ. In short, it is a very Mario - centric theology. Among other things, the Virgin has been declared Co - mediatrix, Co - redemptrix and Co - reparatrix. None of these titles w as unknown in the Roman Catholic tradition, but they had not been made dogmas. Other Palmaria teachings, however, are less traditional.
According to Pope Gregory XVII, the soul of the Virgin was shaped before the creation of heaven and earth. In fact, it had existed in the mind of God eternally. Therefore, the pontiff declared Mary to be God's "companion" in the creation of the world, that she in fact was a co - creator ( PD 34; PKO , 5 , 11 )..
After this, the Palmarians took one further step in declaring that both Christ and the Virgin Mary are present in the Eucharist , as she never left the side of Christ. It is also stated that her presence in the Eucharist is in no was symbolical, but real. Not only the body and blood of Christ is present in the Eucharist, but also the Virgin, kneeling beside him. In one of the papal document this is explained in the following way: We teach as in fallible doctrine that - - - [s]he who is able by grace really and truly to suffer the Sacred Passion of Christ, also by grace is able to be present in the Sacred Eucharist, since, at no moment has Mary ever been, or will be, removed from her Son. (wrldrels.org/articles/palmarian%20catholic%20church/palmarian%20catholic%20church..pdf)
For those unfamiliar with Catholic Eucharistic theology, when the Catholic priest utters the words of consecration over the bread and wine then they lo longer exist, despite the physical evidence of them, for instead that have become the "real" body and blood of Christ that was crucified on the cross, which is consumed by believers in order to obtain spiritual life. Protestants reject this, usually holding to a metaphorical understanding.
