Did Molag Bal and Vivec have a child together? And if so... why? If anyone knows of some primary sources to support this claim I would be very interested as well (i.e. in-game text/books/dialogue). Thanks!

It's fromhttp://www.imperial-library.info/content/thirty-six-lessons-vivec-sermon-twelve (trigger warning for sixual violence on that text. It's Molag Bal, after all). Molag Bal coerced Vivec into it, though the situation as a whole is... Complicated. The children that resulted were monsters (representing Vivec's own flaws) and Vivec spends most of the Sermons hunting them down. I'll let someone smarter than me explain the details

(the censored bits should be fairly obvious)

Your source for this (and about 50% of all mysteries in TES, it sometimes feels) is the 36 Lessons of Vivec. Specifically, http://www.imperial-library.info/content/thirty-six-lessons-vivec-sermon-twelve and http://www.imperial-library.info/content/thirty-six-lessons-vivec-sermon-fourteen:

Here Vivec is seduced by, or willingly submits to, Molag Bal. In fact, they are married in the Pomegranate Banquet. This may represent Vivec submitting to divine authority (Vivec is in love with Bal because of his Daedric nature, outside the natural world) or possibly the opposite: Vivec giving himself over to his own greed and domination. All of the 36 Lessons are allegorical in this way; they represent, through Vivec's lies and secrets, a reality that took place in the new history, where ALMSIVI were always gods rather than taking it through the Heart; but also describe the inner and external struggles of ALMSIVI as they grow into their new divine selves, question who they are and what Morrowind is. Now, in the Pomegranate Banquet, Vivec chooses to marry Molag Bal when the Prince pronounces "CHIM", the syllable of royalty. We are then told:

However, there are nine of these which get special attention in the Sermons. Sermon 14 describes Molag Bal and Vivec making love, and some great orgiastic ritual takes place:

This "race that is no more", the children of Vivec and Molag Bal, are then slain by Vivec with the symbolic spear Muatra:

However, a little http://www.imperial-library.info/content/thirty-six-lessons-vivec-sermon-eighteen, we learn of some of these that have escaped Vivec's killing:The "monsters" born of Vivec's marriage are all highly symbolic and represent ideas and philosophies that Vivec has to overcome. The killing of these takes up much of the rest of the 36 Lessons until (a version of) the war with the Dwemer takes place.

It's worth noting that one of them, the http://www.imperial-library.info/content/thirty-six-lessons-vivec-sermon-twenty-two, was never explicitly said to have been killed. I've heard people suggest that this symbolizes Vivec's own inability or unwillingness to overcome his violent tendencies, but it's up for debate.

You know, not having found every sermon in game, I missed the hole point of him [censored] his own kids to death. Kinda the grossest thing I've ever heard in a game. Why is this character loved so much again?