Kenny compares Momma to Eliot Ness, the cop in the TV show The Untouchables. The show ran from 1959 through 1963, so Kenny and the family would have certainly been familiar with the show. It was about police officers in the 1930's battling organized crime (like old-time gangsters Al Capone or John Dillinger) in Chicago.
When Momma shows up with the following items, Joetta know she's serious this time. (Byron takes a bit longer to figure it out.)
At the beginning of the chapter, Momma says, "I swear that with God as my witness!" Later, she reminds Joetta that she swore to God. First of all, let's be clear. In this case swearing is not the same as cursing. Swearing is to make a promise or take an oath. Cursing is using bad language.
This kind of swearing is a big deal. In the United States, when someone goes to court, they have to put their hand on a Bible and "swear to tell the truth, the whole truth, and nothing but the truth." Lying after taking that oath in court is called perjury, and it's a serious crime. To a religious person, like Momma and Joetta, swearing before God is even a bigger deal based on their religious beliefs.
Other people swear an oath too, like the president in the oath of office saying, “I do solemnly swear that I will faithfully execute the Office of President of the United States, and will to the best of my Ability, preserve, protect and defend the Constitution of the United States." This is President John F. Kennedy taking that oath of office. He was president in 1963.