This isn't about politics; Mukiti is a nature spirit (or whatever the analogous term is in Nyanga folklore) who took Iyangura away from the ordinary world and doesn't want her to go back.
The first piece of evidence is that Mukiti is a somewhat supernatural snake (I didn't mention this in the question because I didn't understand the implications):
Close to the village of Shemwindo [Mwindo's father] there was a river in which there was a pool, and in this pool there was a water serpent, master of the unfathomable. In his dwelling place, in the pool, Mukiti heard the news that downstream from him there was a chief who had a sister called Iyangura.
(all quotes are from A Treasury of African Folklore, the same source of the quotes in the question.)
The second piece of evidence is that once Mukiti marries Iyangura, he traps her in his village while he returns to his supernatural pool. This has nothing to do with Mwindo, who isn't even born yet:
[Mukiti] made a proclamation saying "You, all my people, if one day you see a man going downstream, then you will tear out his spinal column, you Banamaka, Banabirurmba, Banankomo, Banatubusa, and Banampongo; however, this path here which follows the flow of the river, it is the great path on which all people pass."
After he had passed this interdiction regarding these two paths, and while in his village there lives his Shemwami called Kasiyembe, Mukiti told his big headman Kasiyembe: "You, go to dwell with my wife Iyangura at the borders of the pool; and I Mukiti shall from now on always reside here where all the dry leaves collect in flowing down, where all the fallen tree trunks are obstructed in the middle of the pool.
I am still confused by the order about the "path... which follows the flow of the river," but the rest seems clear to me. Mukiti has taken Iyangura to the edge of a supernatural pool, where he will live. He doesn't want anyone to take her from the supernatural world, so he has her live with his headman and instructs his subjects to stop people from approaching the village. I find it extraordinarily relevant that the pool is described as the place "where all the dry leaves collect in flowing down": to me, it suggests that Mukiti and the pool are supernatural and exist at the center of the spiritual universe.
Here are some quotes where Mwindo sings about how he will defeat Mukiti:
For Mukiti shall I get out of my way?
You see I am going to encounter Iyangura,
Iyangury, sister of Shemwindo.
Mukiti, you are powerless against Mwindo.
Mwindo is the Little-one-just-born-he-walked.
This is an interesting story, but unfortunately the book I'm reading it from cuts the story off shortly after Mwindo meets his aunt. I'm going to have to get the full story from somewhere (the book I'm reading excerpts it from The Mwindo Epic, translated and edited by Daniel Biebuyck and Kohombo Mateene).