Welcome to Pitbulls.org › Forums › Pit Bull Talk › Training › Pushing threw to get out the front door and jumping over fence › our pup had the same issues
our pup had the same issues with the door it took some time but now he waits unill he is invited throught the door untill he goes throught ( most of the time )
we started by having him on the leash when we opened the door and if he made it past us we would pull him back and tell him to back it up untill he was invited a couple of times I closed the door on him not hard enought to hurt but firm enought to let him know that it was not ok .
this sounds like just like bad manners just claim the space as yours and dont let him past us blocks / leashes / barriers to help you teach him manners
I have not advice for the fence jumping hope you get that resolved.