It sounds like the yard is more important to you than the square footage or the layout? If so, can you look for a place that has a "den" or "dining room" that can be converted into another bedroom? (Depending on the child welfare laws in your area, you may need to give your child(ren) the actual bedroom with a closet, door that closes, and a window, and then you and DH would sleep in the den/dining room/whatever.)
We currently live upstairs from my mom (she's in a wheelchair, and we help take care of her in exchange for a break on the rent.) But I know that arrangement can't last forever, so I've been researching apartments in our area. Two bedrooms for under $1200 are pretty much impossible to find -- but once we started looking at 1BRs with dining rooms, a lot more possibilities opened up!
Gently, I'd also like to hear what some of you are defining as "dangerous", "ghetto", "shaky", etc... I lived in one neighborhood in NYC that got the "You live THERE?!?!" reaction all the time - but I was right across from a hospital emergency room, and a Dunkin Donuts , so there were CONSTANT police cars parked near my building. I couldn't have felt safer!
In another neighborhood, I had suspicions that a lot of my neighbors were undocumented immigrants - which made me feel pretty safe, as well, since they didn't want any trouble on their block that would have the police asking questions... and the "big men" in that particular community wanted to keep it that way.
All that being said, I've also looked at apartments in neighborhoods that skeeved me out completely - not b/c of the demographics, but because it was desolate after dark, or there was a lot of street harassment of women, etc etc. Really, if you (generic you) are considering a rental, I think the best thing to do is to visit the neighborhood BOTH in the daytime and in the nighttime, and to trust your instincts. Does that make sense?