Non-smokers living with people who smoke suffer the risks of exposure to second-hand smoke. The St. John the Baptist Parish Housing Authority wants to reduce those risks, and cut the cost of building maintenance, by banning smoking inside the agency's public properties. That's a move worth considering.
Corrections suggests that it doesn't suspect non-smokers living with people who smoke are necessarily not-well off. Specifically, we expect that any non-smokers who value a smoke-free household more than the smoker is free to pay the smoker to stop smoking in the household. Being a domestic arrangement, there are low monitoring or enforcement costs. Intra-household transfers are often present enough that every individual has an income of sorts to trade--where they may not pay in dollars, they pay through intra-household transfers, such as cooking, cleaning, television control, etc.
In this case, it appears that in all households where second-hand smoke is present, it is because the smoker values smoking more than the non-smoker values non-smoking. There does not appear to be an externality problem here. Banning smoking would seem to lower smoker's happiness, by definition more than it would increase second-hand smoker's happiness.