Wow you sure have your hands full and I feel for you. If you are willing to tackle all of these issues then more power to you, but my honest opinion is that you are probably in overload. I can well imagine it would be a gut wrenching thing to do, but I think you may all benefit from rehoming the dog if you could find a rescue group maybe who could work with him. I don't think the dog is beyond help by any means, but I just don't see how you can take all of this on with the two babies right now. Again, bravo to you if you can, you're a better woman than I am. I don't doubt your wish to try to right the situation, just your ability given the circumstances. You've gotten some great advice here and I sure do wish you the best of luck with it all. That said, if you feel it's best to part ways with the dog please ask for assistance on the board here on how best to do this. Please do not post an ad in the paper to give him away or sell him. I wish I could offer you some advice, just do what you know is right. Also, you mention a boarding/training situation - don't go there. The true value in training is what the human learns in how to deal with their pets, not what the pets learn. I tried that once with one of my dogs when I had to go out of town so I boarded him at a training facility, I would never do it again.
Good luck to you and