Dean's stubbornness with Jack definitely felt pretty contrived after a while, but I don't think it was all that out of character. Dean prefers to see the world in black and white, and when he is upset he resorts to anger because it's the only emotion he is comfortable expressing. Jack didn't look like a kid, and given what they knew about him at the time they had every reason to believe he would be dangerous. Dean telling Jack that he would kill him after he had seen first hand that Jack didn't mean harm was completely out of line, but I'll forgive him for not being in a rational state of mind. After the third episode it started get pretty ridiculous, though.
It was also nice to see Sam dealing with a kid for a change. Dean tends to be better with kids because he talks to them like they are adults and treats them with the respect most of the grown ups in their lives don't give them. It makes sense because he never got a childhood, so he expects other children to be as mature has he was. That's why Claire, for example, has a stronger connection with him. Sam, on the other hand, was babied more, and to the extent that he was forced to mature beyond his years he feels bitter about being denied his youth. He tries to give kids the sense of security he was missing in his childhood, and as a result talks down to them. This comes off as condescending to most of the teens he has to deal with, but it was more appropriate for Jack who just needed guidance and a parent to tell him everything was okay.