How do you fix a severely mistreated dog, we rescued from neglect and severe abuse?

My husband and I rescued a 5 yr old Jack Russell Terrier from a girl, who had young children, not only was she cruel to the dog, so were her kids. She told us that the home she got her from was even more cruel and neglectful. This dog has a sweet personality, but very unbecoming behaviors and habits. She is what we call a broken dog, she doesn't even know any basic commands. We can not seem to housebreak her. She has been wearing doggy britches and she will still pottys in the house. Some advice would be great, otherwise, we fear our only option for her, is to have her put to sleep. Please help! BTW, we do have another Jack and a Rott...my Jack loves having her around.