This mod alters the two Homeless Households called 'Single Moms', the two household types which are being created again and again after a save game has gone beyond the first day or two.
Where the problem lies with these two household types being chosen over and over again I do not know, I haven't found it; these two household files seem to me to be used as a default selection of some kind 90-95% of the time, the game is ignoring the other household files which are written up in the list of possible household types (inside the filters.neighborhood_population_service file).
Therefore I have chosen a half-baked solution of replacing these two households with two different household types which I have defined, and it is these two which will be generated over and over again instead of the Single Moms. The screenshot below shows both of these household types and also one of the default EA households which are still available when the game is willing to use them. All of these households in the screenshots below were created on day one in a new game.