We tend to associate maggots with disease and uncleanliness, even though in the waking world doctors have successfully used them to treat and prevent gangrene. So it concerns me a little bit that you associate yourself with the maggots. Why would that be? Has someone called you a maggot? This sort of insult is intended to imply weakness and uselessness, and I honestly haven't met many people who deserve to be called this. I doubt that you do, either.

Your small dog, the family pet, can represent quite a bit. A pet is a responsibility, and also a source of affection. The family dog accepts us without question, and loves us unconditionally. What was this dog doing in your dream? This can tell us quite a bit about the true meaning of the symbol.

The bigger dog could possibly represent your father, but again I'm a bit concerned over why this is so. "Big Dog" is a nickname given to the guy in charge, to indicate his importance. For the dog to split into two parts might indicate someone who is trying very hard to do two different things that are mutually exclusive, so that they feel split into two pieces. And when nothing comes out of the dog, that indicates an emptiness inside.

I'm afraid I can't get much farther than this on the images alone. Some actions might help - what was happening, and how did it make you feel?