I don't agree with you that the words "illegal immigrant" create violence. Also, "immigrant" does not carry a negative connotation in most uses as far as I can tell. The negative connotation comes from the word "illegal," which marks someone who commits a crime (illegal immigration) as a criminal. Of course, aside from arrest and deportation, they do not deserve to be subject to violence or maltreatment. That is how every country in the world treats people who immigrate illegally.
I am a second-generation American and actually have been told "go back to your country" and been given the "you don't belong here" before, too. The people who say that shit are assholes and are worth ignoring (it's very easy). But thank you for informing me that disliking the people who jump the line invalidates my perspective.