Why is my pug misbehaving?

I have three dogs, one of them is a pug... my other two are very well behaved (and are both over 100lbs). The pug refuses to go outside to do his business when it's raining, he barks, constantly makes a mess in the house, and can not be trusted off of his leash. He is very healthy according to the Vet, and he has told me that this is typical pug behavior. My other dogs did not have these problems at his age, and I have raised them all the same. Any useful tips?