I rescued an abused dog and he has housebreaking probs...?

He is a year and a half old. I have tried kennel training, no matter how small the space, he will pee and poo in there even if he's just went and done his thing outside.He will literally lay in his own mess. I've tried pee pads...doesn't work. Ive tried tying him up in every room I'm in...again, he will lift a leg on anything. I work from home, so he is with me constantly. I take him out literally every half hour, yet he still does this then cowers and pees some more because he's scared. (i dont punish him). I understand this may be a submissive problem, but reading up on that issue, he doesnt fit the criteria (such as he doesnt pee when greeted, no rolling over, etc) I've tried rewards, still nothing. everything I've tried I've done for months, so gave it a good run. I have taken him to the vet..again, no bladder probs. I'm at my wits end. He is such a little sweety otherwise. At night, I kept him in his kennel beside me, yet he will mess in there. I tried having him sleep with me, but i woke to him peeing on my other pillow. That was the last straw. I'm considering giving him away, but who's going to want a dog with these probs? i feel sorry for him, i cant bear to take him to a shelter, as he has seperation issues. He was formerly owned by a crack addict on the street and has obviously been abused.( He is extremely afraid of anyone raising their voice, and will cower if he senses someones not happy.) Plus, he may not find a loving home and could be euthanized. He is a gorgeous tri colored chiuahuah minpin x. He's playful and rowdy, extremely loyal and protective. A perfect little pet other than this problem. If anyone out there has enough patience to work with him and would be interested in him, please let me know. I really would like to find a wonderful person for him that has experience with rescues.