(Yes, which is why the author labels them as "sexual fugitives")
Anthony W. Ivins was the Juarez stake president from 1896 to 1907 or 08. (He was called to be an Lds "apostle" in 1907).
His son, H. Grant Ivins, wrote a 14-page piece about polygamy in Mexico:
Polygamy in Mexico as Practiced by the Mormon Church, 1895-1905
VERY eye-opening!
{One Lds leader -- part of the top three in the hierarchy of the church instructed Ivins to lie about the Lds practice of polygamy: To indicate the desire on the part of the Church Presidency to keep these marriages secret and even to maintain secrecy as to the practice of polygamy, my father told me, “almost in the same breath, George Q. Cannon said, ‘Now Brother Ivins, if you have occasion to meet Porfio Diaz, President of Mexico, we want you to tell him that we are NOT practicing polygamy in Mexico.” At a much later date, during the Smoot Investigation, my father was invited (I use the word advisedly) to come to Washington and testify that they were not practicing polygamy in Mexico. I use the word “invited” because my father did not go to Washington. He told me that he refused to go on two grounds: “It is none of the Senate’s business what the Mormons we're doing in Mexico, and further, I refused to perjure myself.” (page 2)}
Here's another interesting quote from page 4 of the testimony written by Ivin's son:
That the practice carried on in Mexico was known to the General Authorities cannot be doubted. Many of them visited the Colonies where they could not fail to become aware of what was going on. Among those who came to Mexico on official Church business, some of them many times, were John W. Taylor, Mathias F. Cowley, Hyrum Smith, son of Joseph F. Smith, A. Owen Woodruff, son of Wilford W oodruff, Heber J. Grant, Amasa M. Lyman, B. H. Roberts of the Council of Seventy, and President Joseph F. Smith. These men, with few exceptions, preached with fervor the doctrine that plural marriage was a pre-requisite to celestial exaltation. They urged the young men in the Colonies to accept and practice the principle. Many of them brought pressure to bear on my father to take a second wife, a pressure which he steadfastly resisted. He once said to me, “The Doctrine and Covenants says that those to whom the doctrine is revealed should accept and practice it. It has never been revealed to me that I should do so.” (page 4...link above)
Most of the women came from polygamous families. This was how they lived. They knew the rules. Some women refused to go along with it and some insisted on it.
Essentially, the woman ran the family unit because the father was gone. They liked the being the boss. Some of the fathers were off doing their Mission.
It was an interesting read.
Letters of Catharine Cottam Romney, plural wife / edited by Jennifer M. Hansen.