When it comes down to it, it isn't safe for the OP, her child or the dog to make recommendations regarding this situation on the internet. As she rightly says, we don't know her. What really needs to happen is a professional dog behaviorist needs to visit and see exactly what is going on; what are the triggers for the dog's apparently increased 'aggression', how the OP and her family interact with the dog and how the dog interacts with the family.
The OP's partner chose the boldest dog pup on offer rather than the snugglier bitch pup; he was chosen from an unfortunate location and he is now an adolescent dog pushing the boundaries - the equivalent of the 'terrible twos'. Staffies are smart dogs, they can, do and will learn but they need to be taught and this needs consistency from everybody in the household. They also don't know their own strength at times and this needs to be borne in mind around children.
In short, arguing on a forum isn't going to help, there needs to be a physical visit from a qualified person (there have been links posted already) to actually see what's going on and make recommendations accordingly. If the recommendation is that the dog can and should be rehomed then it can be explained to the OP the best way to go about it. Likewise if the behaviourist thinks the dog can be properly integrated into family life then this will be explained.
The dog is also showing signs of stress and possible separation anxiety (the OP describes him as 'clingy'), peeing in his crate when left though otherwise apparently housetrained. If the OP isn't happy, you can bet the dog isn't happy either.
Trying to rehome a Staffy which 'bites' will not be easy. The behaviour needs to be seen and understood before taking any action other than separating the dog from the child for safety until this can take place. As other posters have said, these things rarely happen 'out of the blue' but often there is a solution.