I think "you should not" sounds more natural, why is he using "you're not gonna" in this sentence?
"Should not" is a conditional here and indicates that one has a choice to do something, but they shouldn't do it. "You're not gonna" indicates that someone doesn't even have a choice to do something because they will be stopped or forced to not do it. "You're not gonna" is similar in this case to "I'm not going to let you." It is used here to give a stronger impression that she doesn't have a choice and is not going to get away to twisting everything he says.