For one, stop calling HIM the Alpha. YOU should be the Alpha in the home, YOU should be the one in control of the home, NOT the dog.
First and foremost, set firm boundaries for him. The very MOMENT he lifts his leg, give him a firm "no" and set him outside. Look into the NILIF training method for some extra help.
Second, find any and EVERY spot he's marked, clean it well with either vinegar or bleach to completley remove the scent. The less of himself he smells in the house, the less likely he is to remark any spots.
Training, training, and more training. If needed, hire a professional trainer or behaviorist to assist you. There's really no 'special trick' to becoming the pack leader in your own home. Train and treat him just the same as you would a large breed of dog. Don't let his size fool or mislead you, he's still a DOG, and needs to be treated like a DOG of any size. No dog should be treated differently due to their size, etc... because they're still DOGS. Don't allow him to be the Alpha. Assert YOURSELF as Alpha, and that will do a world of good.
ETA: @ Josh - Read the whole question, the dog has already been neutered. Also, spaying/neutering doesn't always help in a situation where the dog thinks THEY are in control rather then knowing that the HUMAN is in control.
On a side note, forgive the caps, I'm not yelling, I'm trying to emphasize, lol