I think this is the problem with the young woman who wants to join the Church of Jesus Christ of Latter-day Saints. You said, "She doesn't want to give up all her Mormon training and teachings to join a church that doesn't believe in the things she was brought up to believe in, which she would have to do if she went to any regular Protestant denomination. " The truth is that there isn't some other "Mormon" church which has the same beliefs, but also believes in polygamy. I was just looking at some of the beliefs of groups who splintered off from The Church of Jesus Christ of Latter-day Saints. Their beliefs are really different!!
See https://www.mormon.org/ "Beliefs" for "Mormon" beliefs.
These other religions do read the Book of Mormon, but do not consider it equal scripture with Bible.
They have a person who calls himself a "Prophet" who chooses his own successor, not God.
They mainly have lay ministers, which they call "Priesthood"; some are paid and some are elected to office.
You need to know a little history. In the early days of the Church of Jesus Christ of Latter-day Saints, there were members who left the Church after Joseph Smith was killed. Instead of following the new prophet chosen by God, they set up a dynasty choosing a descendent of Joseph Smith to be their leader. Not only did they not join the other members heading west, but they returned to many of their old religious beliefs such as the Trinity, keeping a few things they liked such as the Book of Mormons.
It is a little like the Samaritans. Through contact and intermarriage they ended up with a religion which was made of foreign beliefs mingled with Jewish law and tradition. The Jewish people have diligently tried for generations to maintain their true beliefs. They do not consider someone who has read the Tora a Jew, and neither do we consider a person who has read the Book of Mormon a member of our faith.
We believe in the same true Gospel that was given by God to Abraham, Moses, and the other prophets the Lord has chosen. We do not believe in a religion based on the Book of Mormon mingled with Christian tradition.
The religion these polygamists practice has only a slight resemblance to the beliefs of The Church of Jesus Christ of Latter-day Saints. Though this woman was raised with the Book of Mormon in her home, that does not mean that she knows anything about our beliefs. She couldn't have had "Mormon training". She could only have had a Book of Mormon. I could not find any of their beliefs that were the same as the beliefs of The Church of Jesus Christ of Latter-day Saints. She can't continue to be a "Mormon", because she never was one. Like every other convert, she must first learn our beliefs and commit to living the teachings of the Church before she can become a member.