The practice of Polygamy within the church was stopped in 1890 by the prophet Lorenzo Snow. This can be read in Official Declaration 1. Where the prophet prayed about the circumstances that the church were facing and as answer to their prayers were told to stop, With the statement by president Woodruff "But I want to say this: I should have let all the temples go out of our hands; I should have gone to prison myself, and let every other man go there, had not the God of heaven commanded me to do what I did do; and when the hour came that I was commanded to do that, it was all clear to me. I went before the Lord, and I wrote what the Lord told me to write."
The social taboo on Polygamy is completely understandable in the society we live in it is seen as adultery. And in the revlation given to Joseph Smith he was told that without the concent from the first wife it is against God's commandments. It says this in Doctrine and Covenants 132:61.
As with all of God's commandments we may not always understand why he gives them to us. But if we prayerfully consider what we have received from Him, Pray about it and be willing to act on what God has told us than we will know what He wants for us and we will know the truth of a matter.