As with any religion there are those adherents who will take things to the extreme. Examples: snake handling, speaking in tongues, polygamy, yada yada. I'm sure not all Mormons subscribe to the wifely submission thing, just as all Baptists do not but there are those who do.
My Baptist aunt is a staunch believer that the man should run the household 100% and the wife should never question his authority. That's based on Ephesians 5:21-32.
,b.21 and be subject to one another in the fear of Christ. 22 Wives, be subject to your own husbands, as to the Lord. 23 For the husband is the head of the wife, as Christ also is the head of the church, He Himself being the Savior of the body. 24 But as the church is subject to Christ, so also the wives ought to be to their husbands in everything. 25 Husbands, love your wives, just as Christ also loved the church and gave Himself up for her; 26 that He might sanctify her, having cleansed her by the washing of water with the word, 27 that He might present to Himself the church in all her glory, having no spot or wrinkle or any such thing; but that she should be holy and blameless. 28 So husbands ought also to love their own wives as their own bodies. He who loves his own wife loves himself; 29 for no one ever hated his own flesh, but nourishes and cherishes it, just as Christ also does the church, 30 because we are members of His body. 31 For this cause a man shall leave his father and mother, and shall cleave to his wife; and the two shall become one flesh. 32 This mystery is great; but I am speaking with reference to Christ and the church. 33 Nevertheless let each individual among you also love his own wife even as himself; and let the wife see to it that she respect her husband.
So the husband should love the wife but in the end she is expected to submit to his wishes and commands. Hmmm. Wouldn't work in my house for sure.
I've never read the Book of Mormon so I'm not qualified to comment on that. It seems that the whole polygamy and submisison thing are wound up in Joseph Smith deciding his wife Emma wasn't enough and then commanding her to allow him to step out, but there's no hard proof of this that I can find.