St. Paul says, "and the hope shall not be ashamed, because the love of God is poured out in our hearts by the Holy Spirit which is given unto us." (Rom 5:5)
And here is the passage in St. Augustine you are talking about, which itself should clear up some of the questions: "I know not why both the Father and the Son and the Holy Spirit should not be called Love, and all together one love, just as both the Father and the Son and the Holy Spirit is called Wisdom, and all together not three, but one wisdom. For so also both the Father is God, and the Son God, and the Holy Ghost God, and all three together one God. 29. And yet it is not to no purpose that in this Trinity the Son and none other is called the Word of God, and the Holy Spirit and none other the Gift of God, and God the Father alone is He from whom the Word is born, and from whom the Holy Spirit principally proceeds. And therefore I have added the word principally, because we find that the Holy Spirit proceeds from the Son also. But the Father gave Him this too, not as to one already existing, and not yet having it; but whatever He gave to the only-begotten Word, He gave by begetting Him. Therefore He so begot Him as that the common Gift should proceed from Him also, and the Holy Spirit should be the Spirit of both. This distinction, then, of the inseparable Trinity is not to be merely accepted in passing, but to be carefully considered; for hence it was that the Word of God was specially called also the Wisdom of God, although both Father and Holy Spirit are wisdom. If, then, any one of the three is to be specially called Love, what more fitting than that it should be the Holy Spirit?— namely, that in that simple and highest nature, substance should not be one thing and love another, but that substance itself should be love, and love itself should be substance, whether in the Father, or in the Son, or in the Holy Spirit; and yet that the Holy Spirit should be specially called Love." (On the Trinity, Book 15, Chapter 17,— How the Holy Spirit is Called Love, and Whether He Alone is So Called. That the Holy Spirit is in the Scriptures Properly Called by the Name of Love.
http://www.newadvent.org/fathers/130115.htm)
John 17 says that if you are predisposed to view any time when Jesus talks about the love that His Father has for Him in the light of St. Augustine's idea, which you already affirm. But that's not me, and I must again point out that if this is meant to be understood with St. Augustine's peculiar idea in mind, then we have a problem, because in 17:26, Jesus prays "And I have declared to them Your name, and will declare it, that the love with which You loved Me may be in them, and I in them.”
Who in your understanding is "the Love with which you loved Me"? Jesus speaks of Love as a Person and says this Person will be in the Apostles along with Him. Thus, it is quite consistent exegesis to understand this of the Holy Spirit (in a special way, just as the Son is called Word and Wisdom in a special way in the Scriptures, though both Father and Holy Spirit are also Wisdom) especially in light of "the love of God is poured out in our hearts by the Holy Spirit which is given unto us" (Rom 5:5, cited above). Jesus asked that the Holy Spirit would be granted to us His disciples and the Father heard His prayer and gave us the Spirit of adoption, "Because you are his sons, God sent the Spirit of his Son into our hearts, the Spirit who calls out, "Abba, Father." (Gal 4:6)
If the Holy Spirit, as a Person of the Holy Trinity, is the bond of love between the Father and the Son (i.e., if that is His essence), then is Jesus saying here that we are to make up the third Person of the Holy Trinity, as we are to share in the love manifested between the Father and Son
Not at all. As Jesus was the eternally beloved Son of the Father by nature, we become in time the sons of God through the grace of the Spirit given to us. The One Who unites the Father and the Son in eternal Love now unites God with each individual son or daughter through grace. We distinguish how God is in Himself, and how He communicates Himself to us. The word "energies" in the East is usually translated as "operations" in the West, or sometimes simply grace. God acts on us by His operations and divinizes us by His grace. Kindly see this dictionary as evidence the same concept, in slightly different terminology, is present in the West:
https://www.catholicculture.org/culture/library/dictionary/index.cfm?id=33161But we don't need to go to St. Augustine, we can discuss the teaching of two great authorities, one Latin and one Alexandrian.
Bishop St. Ambrose of Milan: "The Holy Spirit also, when He proceeds from the Father and the Son, is not separated from the Father nor separated from the Son. For how could He be separated from the Father Who is the Spirit of His mouth? Which is certainly both a proof of His eternity, and expresses the Unity of this Godhead." See
http://catholicpatristics.blogspot.com/2009/08/filioque.htmlPatriarch St. Cyril of Alexandria: "For, in that the Son is God, and from God according to nature (for He has had His birth from God the Father), the Spirit is both proper to Him and in Him and from Him, just as, to be sure, the same thing is understood to hold true in the case of God the Father Himself." (Commentary on the Prophet Joel 35 [PG 71:377D]). Please read the link for more details. Even in the first 500 years of unity between the Catholic Church and Oriental Churches, there are other testimonies - for e.g. that of Bishop St. Leontius of Caesarea at Nicaea I. The Liturgy of St. Mark, first Patriarch of Alexandria, also confirms that Unity in the Holy Trinity is attributed in a special way to the Holy Spirit: "One Father holy, one Son holy, one Spirit holy, in the unity of the Holy Spirit. Amen."
http://www.newadvent.org/fathers/0718.htm