I have one mom. I have 2 grandmas, and assuming that your mom and dad aren't brother and sister, you have two grandmas also.
No, the LDS church does not practice polygamy. No, the FLDS church is not affiliated with the Church of Jesus Christ of Latter-day Saints (LDS church).
The church has an official statement on polygamy which says this:
Today, the practice of polygamy is strictly prohibited in the Church, as it has been for over 120 years. Polygamy — or more correctly polygyny, the marriage of more than one woman to the same man — was a part of the teachings of The Church of Jesus Christ of Latter-day Saints for a half-century. The practice began during the lifetime of Joseph Smith but became publicly and widely known during the time of Brigham Young.
It is hard enough for a man to support one family, let alone several.
And I deeply admire the women who worked so hard to take care of their kids and support each other while their husbands were gone.
Our church today and in the past has really emphasized the importance of family and the roles of fathers and mothers and that their spouse and their children must be their number one priority. In fact, the LDS church has issued a Proclamation to the World on Family. (found here https://www.lds.org/topics/family-proclamation)
I don't know all the reasons why God asked the members of the early LDS church to practice polygamy but I know a few of the reasons. There were a lot of women joining the church; some of whom were leaving drunk, abusive husbands in Europe. Legally and financially and physically, it was impossible for these many single women to make the trip to Utah where they would be free from religious persecution.
As I said, I really admire these women for the sacrifices that they made in following what they believed to be true, despite the difficulties of the situation. I think it was easier to be someones 3rd wife, than to be no ones wife and have no man to take care of your kids. Obviously it is ideal that a mother and father take care and raise their kids in love. I'm just so glad that the time frame for polygamy was short and I think it served its purpose even though I don't know all of the details of its purpose (God knows so much more than I do!)
But honestly and realistically, I can't imagine sharing my husband Matt. The army already kinda acts as a second and third wife .