The Home is the orphanage where Bud is currently living. He lives there with many other children that are waiting for foster parents to adopt them. Bud is 10-years-old and has been in and out of foster homes a few times.
Bud does want to go back there. In chapter 1, a foster family has been found for Bud. Bud is immediately suspicious of the family, because they already have a 12-year-old boy. Bud knows that the boy is going to try to assert his dominance. And that's exactly what happened. The older boy, Todd, shoved a pencil up Buddy's nose. Buddy retaliated. Todd retaliated by kicking and kicking Bud. Todd's mom, Mrs. Amos, saw the confrontation, believed Todd's lie about it, and threatened to return Bud to the orphanage home. Buddy begs not to be sent back there, but admits (to the reader) that he was lying. He has learned that adults tend to take away the things that you want as a threat. So if Bud begs not to be sent away and stay at the house, then they will send him back. That's exactly what Bud wants, so he doesn't have to stay in a home in which he is beat and abused by an older sibling and mother who doesn't treat Bud equally.
I looked up and could see she needed more. "If you give me another chance I promise I’ll do a whole lot better. Please don't call the Home, please don't send me back." Shucks, going back to the Home was just what I wanted to do, but I was being just like Brer Rabbit in one of the books Momma used to read to me at night when he yelled out, "Please, Brer Fox, don't throw me into the pricker patch, please, please!"