Doesn’t John 20:17 prove that the Father is a separate god from the Son or that the Son is not God?
Simply because Jesus refers to His Father in John 20:17 as "my God, and your God" is no reason to assume polytheism (i.e., there is more than one true God). The passage never uses the term "Gods" nor does it expressly state that there is more than one true God. Further, the passage never claims that Jesus is not the only God. It merely claims that Jesus and others had a God. But then how could Jesus be God if He claims He follows someone other than Himself (namely, the Father) as God?
This passage must be understood in its context. Just a few chapters earlier Jesus had taught that there is an "only true God" (Jn. 17:3). Later in the John 20 passage, Jesus accepts the title of "God" from Thomas and commends those who would also believe without having Jesus appear to them (vss. 28-29). Even the title page of the Book of Mormon calls Jesus "the Eternal God," and Alma 11:24-31 says that there is not more than one God (not a "Godhead" team of separate gods since the third person singular--"him"--is used in verse 24, and because D&C 20:19 says that the only living and true God is the only being that is to be worshipped). Since Jesus is not a false god, He must be the only true God Being just as much as the Father is. But what sense does this make?
This makes sense to those who hold to the Christian doctrine of the Trinity. Elsewhere I described this doctrine as "within the nature of the only Being of God there is, there forever exists three different, albeit inseparable, Persons--Father, Son, and Holy Spirit." Thus, since the Being of God has more than one person, there is nothing incoherent about one of the members referring to another as His God. For an example of the Father calling the Son "God," see Hebrews 1:5-13. This God cannot be a false God, since He is, in contrast to all the angels, begotten of the Father, commanded to be worshipped by the Father (cf. Matthew 4:10), and the One who laid out the heavens and the earth (cf. Isaiah 44:24). The Son of God must be inseparably united with the Father of God from eternity to eternity. In Mormonism, on the other hand, the Father hasn't always been inseparably united with the Son, since the Father had to first impregnate a wife.
The only problem left is our non-biblical assumptions as to what God must be. For those who are neither serious students of the Bible nor are deeply in love with God’s word, it simply seems bizarre that God would be so unique as to be a three member Being. Joseph Smith ridiculed the doctrine by saying, "Many men say there is one God; the Father, the Son and the Holy Ghost are only one God! I say that is a strange God anyhow—three in one, and one in three! It is a curious organization. ...All are to be crammed into one God, according to sectarianism. It would make the biggest God in all the world. He would be a wonderfully big God—he would be a giant or a monster" (History of the Church 6:476). The natural man wants to put God in his own image--to make Him more commonplace. But those who truly have a heart for God and His word must continually humble themselves in realizing that the Lord told us long ago, "For my thoughts are not your thoughts, neither are your ways my ways" (Isa. 55:8).
Certainly analogies may help. St. Patrick reportedly was quite successful in converting the pagans in Ireland using the analogy of the shamrock to explain the Trinity. But if God reveals Himself as a triune Being, then whether it makes sense or not is not really the issue. The issue boils down to simply one of trust. Will we take the Omnipotent at His word or not, realizing that "without faith it is impossible to please him" (Heb. 11:6)?
R. M. Sivulka