If his purpose for pulling over, and running alongside of her, was so he could ask her on a date, and she told him 'NO, go away please'---he would have no reason to throw her in the trunk of his car. He could have just left her alone.
She was not going to call the cops unless he kept following and harassing her. He could have stopped.
But he didn't stop because he was not there just to flirt or ask her to dinner.
However if we go with your scenario, and he only reacted that way because he was worried ABOUT LOSING WHAT HE HAD---then I am afraid that he is a monster.
He is the one that is breaking our laws, living here illegally, using stolen identity to stay here and work. Those are his own choices. And when he aggressively pursues a woman, to the point she feels the need to call 911, he decides to KILL HER, to cover up his previous crimes.
That is not the description of a 'regular, good guy.' That describes a violent criminal with no conscience, IMO.