If the Trinity doctrine were true, Jesus would most surely have used the word and taught the doctrine exactly as it appears in the Nicene creed–but He didn’t do that. Instead, He allowed the Jewish leaders to take what they knew from the Old Testament and reject Him as the Savior and the God of Israel, their King. Instead also, He taught them to pray to Father in Heaven, in the name of Jesus Christ. He introduced that teaching even though they were familiar with praying, and did pray.
He didn’t teach the Trinity doctrine. He did teach that He and His Father are One, so They are indeed One God. He also prayed that His followers can be one with Them, very specifically and in the same instance when He said that He and His Father are One.
Jesus was never meant to reign over the Jews as a king on earth. He came to save them from their sins. Their mistake was due to a misinterpretation of scriptures about the Messiah. He was meant to be their spiritual Savior and Heavenly King, from the very beginning. But, due to their carnal nature and way of thinking, they thought He’d come to save them from their earthly enemies, by destroying them.
Jesus did teach the mystery of the Trinity to the Apostles, but even they had a hard time understanding it. There are also references in the Bible, even if that term isn’t used.
[1 John 5:] [6] This is he that came by water and blood, Jesus Christ: not by water only, but by water and blood. And it is the Spirit which testifieth, that Christ is the truth. [7] **And there are three who give testimony in heaven, the Father, the Word, and the Holy Ghost.
And these three are one.**Just because Joseph Smith couldn’t understand that theological concept, or accept the fact that those Three could really be One God, doesn’t mean that he was correct in his assumption that They are only One ‘in purpose’. His concept is not of Him being one ‘god’, but three separate ‘gods’, which is classic polytheism, even though LDS always deny that fact. He was wrong because there is only One God, and He is a Holy Trinity.
St. John even said that if all of the things that Jesus said and did were to be written, that the world could never hold all of those books. He taught them much more than was included in the New Testament scriptures. That’s what the Deposit of Faith, and the Holy Tradition of the Church, are all about. Many of those other teachings can only be found there, in the Catholic Church.
As to the part of your comments that I’ve placed in bold, Jesus never said anything like that.
[Matthew 6:] [8] Be not you therefore like to them, for your Father knoweth what is needful for you, before you ask him. [9] Thus therefore shall you pray: Our Father who art in heaven, hallowed be thy name. [10] Thy kingdom come. Thy will be done on earth as it is in heaven.
[11] Give us this day our supersubstantial bread*. [12] And forgive us our debts, as we also forgive our debtors. [13] And lead us not into temptation. But deliver us from evil. Amen.*Note: The “supersubstantial bread” mentioned in His prayer refers to the Holy Eucharist that Jesus encourages us to receive, daily, and not just once a week, or occasionally. The Douay-Rheims originally translated it this way, even though most other Bibles only include the word “bread”, which might seem to only refer to asking for our earthly sustenance.
Jesus never said that we should only pray to the Father, nor did He ever say that we should only pray in His name. He just gave us one example of how we should pray. Since He is God, there’s no reason not pray to Jesus. In fact, in the same epistle of John, he makes it clear that we should pray to Jesus, Himself.
[1 John 5:] [11] And this is the testimony, that God hath given to us eternal life. And this life is in his Son. [12] He that hath the Son, hath life. He that hath not the Son, hath not life. [13] These things I write to you, that you may know that you have eternal life, you who believe in the name of the Son of God. [14]
And this is the confidence which we have towards him: That, whatsoever we shall ask according to his will, he heareth us. [15] And we know that he heareth us whatsoever we ask: we know that we have the petitions which we request of him. I don’t think there can be any doubt that John was telling us that we also can, and should, pray directly to Jesus for whatever we need. He will always hear our prayers.
So there is the difference. Latter-day Saints pray to Father in Heaven, in the name of Jesus Christ, and believe and know that They are One God, and that Jesus taught specifically to pray to Father in Heaven, in the name of Jesus Christ. Latter-day Saints also understand that Jesus was praying that His followers would be able, through His atoning grace (saying His mighty, High Priestly intercessory prayer just before taking upon Himself the sins of the world and thus atoning for the sins of all mankind on condition of personal repentance), to be one with Them. It is a prayer we are not afraid to understand literally, and are aware that it takes great faith to believe literally in Jesus’ divine commission to bring us to God with the power to become one with Them. But we don’t fear that divine commission He received and carried out–we have faith in His truthfulness, and in His power to do what He was sent to earth to do.
Being one with God is to share in His eternal life, in Heaven, where we will all enjoy His company, together with our family and friends, as well as all of the angels and Saints. There’s nothing more that we would ever need to be completely happy, forever.