Just so we are clear on what Fox is saying about Michele Obama, let's consult
UrbanDictionary.com for a definition of "baby mama".
1) The mother of your child(ren), whom you did not marry and with whom you are not currently involved.
2) A term used to define an unmarried young woman (but can be a woman of any age) who has had a child. As mentioned before in another definition, most of the time it is used for when it was simply a sexual relationship, compared to ex-wife or girlfriend. Usually this has a negative connotation, a lot of baby mamas are seen as desperate, gold digging, emotionally starved, shady women who had a baby out of spite or to keep a man. Sometimes they may act like this because of missed child support payments, unfulfilled promises by the father, or convenient sex by the father. Either or both may exist in any situation.
An article in Slate
delves further into the etymology:
The Oxford English Dictionary defines baby-daddy as "the father of a woman's child, who is not her husband or (in most cases) her current or exclusive partner." The baby-mama entry follows the same template with the genders reversed.
The OED lists baby-daddy and baby-mama as "colloquial, chiefly African-American" variants of the Jamaican terms baby-father and baby-mother; its first citation for baby-mother hails from the Kingston Daily Gleaner in 1966.
If you called your husband your "baby-father," he might be insulted—the term suggests biological fatherhood in the absence of any real parenting. The linguistics professor Peter L. Patrick, who studies Jamaican Creole, said the terms "definitely imply there is not a marriage—not even a common-law marriage—but rather that the child is an 'outside' child."
Now, are we clear what Fox is saying when it puts this on the screen?