You'd probably be correct, except that "Elohim" is a noun, not an adjective like "divine" is, and the order of the Hebrew words does not match that translation.
The SOURCE of the Sons' authority is God.
No argument there, though you could also say that the source of His authority is Himself, since He is God.
In fact, can't you see at all that in the very next verse it says, "That is why God, YOUR GOD has anointed you with the oil of exultation..."
You love righteousness and hate wickedness; Therefore God, Your God, has anointed You With the oil of gladness more than Your companions. - Psalm 45:7
http://www.biblegateway.com/passage/?search=Psalm45:7&version=NKJV
If you're looking at JUST those two verses, and knew nothing about Hebrew or the rest of the Bible, they would seemingly contradict one another, because in verse six it calls the Son God, and in verse 7 it calls the Father God. How could that be if there is only ONE God?
Those two verses together only make sense if God is a plurality, having more than one person in the Godhead.
If the Son was God, how could he HAVE a God?
God the Son's God is His Father God.
The Son willingly submits Himself to the Father, in effect making His Father His God. This is why God says for us to honor our parents, because Jesus honors his Father, and God (the trinity) wants us to be like Him.
Someone really messed up that translation from Psalm 45. They try to say the Son is God, and yet he HAS a God! Really, JR? Can you think?
Again, I provided you with the Hebrew scripture. If you can show that the original texts say something different (in Hebrew, not English) than what I provided above, then you will have evidence that the scripture was mistranslated. But until then, I'm going to go with what I have provided, which says "your throne, O God, is forever and ever."
Oh, I almost forgot to discuss Hebrews 1:8... Back to Greek and English we go, because "To the Hebrews" (as far as I can tell) was originally written in Greek, not Hebrew or Aramaic...
But to the Son He says: “Your throne, O God, is forever and ever; A scepter of righteousness is the scepter of Your kingdom. - Hebrews 1:8
http://www.biblegateway.com/passage/?search=Hebrews1:8&version=NKJV
But de regarding pros the ho Son hyios he says, · ho “ Your sy throne thronos, O ho God theos , is for eis all ho time ai?n ho , · ho and kai the ho scepter rhabdos of ho absolute justice euthut?s is the scepter rhabdos of ho your sy kingdom basileia . - Hebrews 1:8
http://www.biblegateway.com/passage/?search=Hebrews1:8&version=MOUNCE
"DE PROS HO HYOS HO SY THRONOS HO THEOS EIS HO AION HO"
"[But] [regarding] [the] [Son] he says, "[Your] [throne], [the God], [is for] [all] [time]."
Again, "ho" is the definite article "the" in Greek. There is no word for "a", such as "a God." You would only say "theos" for "a god," not "ho theos," which means "The God," and that refers to the one true God.
"SY THRONOS HO THEOS"
"Your Throne, the God"