Dear friend,
The Catechism of the Catholic Church defines grace in this way: “Grace is favor, the free and undeserved help that God gives us to respond to his call to become children of God, adoptive sons, partakers of the divine nature and of eternal life.” (#1996) It is always best for us to use the terms the Church uses in the way the Church uses them. Strictly speaking, the Church would say that grace is the EFFECT of the indwelling of the Holy Spirit and not the indwelling itself.
As for identifying the Trinity with the Real Presence of Jesus in the Eucharist, we must recognize that the Eucharist is the body and blood of Jesus only. The Father and the Holy Spirit are spirits and do not have bodies. They did not become incarnate. While the whole divine economy is the common work of the three divine persons, the Catechism tells us: “each divine person performs the common work according to his unique personal property.” (#258) So while Jesus is one with the Father and the Holy Spirit and co-equal with them, we only speak of the Eucharist, and therefore the Real Presence, in terms of HIS body. The indwelling presence of the whole Trinity is a spiritual presence and not an incarnate one.
Fr. Vincent Serpa, O.P.