Honestly? If you can afford the house you live in now, even if it's tight in other areas, IMO it would be an incredibly poor decision to move into government subsidized low-income housing. I haven't lived in it, but I grew up on the outskirts of it and I'm living on the outskirts of it right now, and there's no way I'd willingly move into it and expose my children to that. The highest-crime areas of a city are the lowest-income areas, and what I have seen is that the government-subsidized areas are the worst. Subsidized housing almost always means high amounts of violent crime, drug crime, high school drop-outs, and teen pregnancy. When I was a teenager we very briefly--as in, for about two weeks--lived across the street from government-subsidized housing. During that time our house was broken into twice (they didn't steal anything only because we had nothing worth stealing), and we got to go to sleep listening to shooting every single night. I'm safe enough where I am at the moment, but the subdivision I live outside of is heavily Section 8 (not what you're going for, I know, but subsidized rents nonetheless). The sheriff's office warned us against going into that neighborhood after dark. I have an acquaintance who lives in the neighborhood, and she's reported such things as someone having their television stolen in broad daylight with people watching.
Maybe, if you live in a small town with little to no violent crime, you'll be OK. But the drug problem is widespread, and it breeds violence. And there's no way I'd want to be a single woman living in subsidized housing. It's probably better than living on the street, but it's not something I'd aim for.
If you hunt, really hunt, you may well be able to find something more affordable than where you are now that isn't subsidized. With only one child, you may well be able to rent a studio apartment or a 1-bedroom. I've noticed that there's a large amount of cheap apartments available very near the community college I attend--my best friend had a darling almost-studio apartment in an old house in an historic district for $325/month. These things typically are not advertised in newspapers--other than small, free neighborhood circulars--or online. Going on foot or driving around looking for For Rent signs is how they're found. The bonus is that a lot of times you will be able to find a landlord who is willing to rent to you without a credit check--our current landlord is one of them.