Herbicide that won't hurt animals or insects?

Okay, I've just discovered that we have a weed in our yard that Buddha is pretty allergic to. I've also got, for the first time in my life, a poison ivy/oak/sumac rash. Obviously, I need to do some weed elimination in our yard. But we have Buddha, and our next door neighbor's cat, Sheena, and all the birds and beneficial insects and birdfood insects to think about. Bayer has some herbicides http://www.bayeradvanced.com/productFamily/lawn-weed-control.html and http://www.bayeradvanced.com/product/Brush-Killer-Plus/ that look hopeful, but I want to make sure the only thing they'll kill is the weeds they're supposed to kill.

Corn gluten meal isn't really an option because it doesn't work against established weeds, and our backyard is pretty much all established weeds.

I definitely have to do something though, otherwise we won't be able to go out into our yard.