I appreciate you giving the versus as I have never heard of God authorizing divorce as Jesus says the opposite. .
Here is a good example of having two wives
Exodus 20:1
And God spoke all these words:
Then jump to 21:9
"If he selects her for his son, he must grant her the rights of a daughter. 10 If he marries another woman, he must not deprive the first one of her food, clothing and marital
rights. 11 If he does not provide her with these three things, she is to go free, without any payment of money."
As far as Deuteronomy, it should be read as a book. Moses is speaking, but he is relaying the words that God spoke to him. As it is Sacred Scripture, we can discard the idea that Moses was lying through his teeth.
So here are a few places where Moses credited God with the giving of this law
4:1-2,5
Now, Israel, hear the decrees and laws I am about to teach you. Follow them so that you may live and may go in and take possession of the land the Lord, the God of your ancestors, is giving you. 2 Do not add to what I command you and do not subtract from it, but keep the commands of the Lord your God that I give you…See, I have taught you decrees and laws as the Lord my God commanded me, so that you may follow them in the land you are entering to take possession of it
6:1-2
These are the commands, decrees and laws the Lord your God directed me to teach you to observe in the land that you are crossing the Jordan to possess, 2 so that you, your children and their children after them may fear the Lord your God as long as you live by keeping all his decrees and commands that I give you, and so that you may enjoy long life.
8:6
Observe the commands of the Lord your God, walking in obedience to him and revering him.
11:1
Love the Lord your God and keep his requirements, his decrees, his laws and his commands always.
Anyway, that is the point of Deuteronomy. Yes, they called Moses the Lawgiver and called it the Law of Moses, but there was always the understanding it came straight from God. Even today, while we number the Ten Commandments differently, we hold them in reverence as straight from God.
What I find ironic is that in most areas of contrast between Jehovah in the Old Testament and Jesus in the New, it is almost always (every thing but divorce) the God of the Old Testament that is seen as wrathful and gentle Jesus that is seen as merciful. The truth, as we know, is that there is but one God and there is no division of will. As Jesus never contradicted the Mosaic Law, understanding the differences can yield insight in all areas as to what is absolute and what is not. Theologians do not disregard this important data like this. Thus we have disagreement between two orthodox bishops, like Kasper and Burke.
The Church teaches black and white truth, yet we are also still in need of the Holy Spirit leading us into more truth. That is because not everything is known. That which is not known is not black and white doctrine. I will not call it gray, but rather magenta.