This is one of the trickiest topics to discuss with a Mormon.
For one, they think "one in purpose" sufficiently places them in monotheism. Wonderful doubletalk. I suggest presenting Joseph Smith's view on the matter:
" I have always declared God to be a distinct personage, Jesus Christ a separate and distinct personage from God the Father, and the Holy Ghost was a distinct personage and a Spirit: and these three constitute three distinct personages and three Gods. If this is in accordance with the New Testament, lo and behold! we have three Gods anyhow, and they are plural; and who can contradict it?" -Teachings of the Prophet Joseph Smith, pp. 370
If they pull the opinion card, I'd stress how a polytheist came up with their "we can become gods" doctrine. Wonder what else Smith came up with around that time...I'll have to look up the time that Smith's new view happened, I believe it was around the time he first studied Hebrew and mistranslated Elohim in Genesis. Aomin.org has a good article on that.
But take a look at Bruce McConkie's views:
"Three separate personages-Father, Son, and Holy Ghost- comprise the Godhead. As each of these persons is a God, it is evident, from this standpoint alone, that a plurality of Gods exists. To us, speaking in the proper finite sense, these three are the only Gods we worship. But in addition there is an infinite number of holy personages, drawn from worlds without number, who have passed on to exaltation and are thus gods." -Mormon Doctrine, pp. 576-77
But look what McConkie does to himself, even in the same book! It's ridiculous:
"Monotheism is the doctrine or belief that there is but one God. If this is properly interpreted to mean that the Father, the Son, and Holy Ghost-each of whom is a separate and distinct godly personage-are one God, meaning one Godhead, then true saints are monotheists."
They want to have their cake and eat it!
Furthermore, as it is with almost ANYone who questions the Nicene Creed, explaining the trinity to them is like walking through a minefield. It's difficult, especially in person, to remember the verses that prove the "three persons in one being" concept and then to logically justify a "three persons in one" concept. I can imagine a modern-day evangelical layperson making a mockery out of the trinity while discussing it to a Mormon. I mean really, do we only get to learn about this doctrine through some seminary school? Thank God for the Internet.
And though Mormons are theistically confused, let's keep in mind they have a hard time distinguishing between "wisdom" and "knowledge" in the first place--an error that, had it been correctly thought out, would've saved them from the mess they're in. Heck, we almost need to distinguish "feeling" from "knowledge" while we're at it!
God help us.
And Obiwan, to answer your question, LDS vehemently oppose Nicene trinitarianism. I'm not sure what you meant by social or economic trinitarianism, so I just went with what it essentially is. In fact, I'm pretty sure anything that strays from Nicene trinitarianism has a different name than trinitarianism. I'm not big on differentiating the names of different doctrines (only the principles of them), so here's a good article on the different names: http://vintage.aomin.org/trinitydef.html