Sorry, writers, but you could not convince me to like Laurel.
She chose not to get any kind of medical attention for her son after he was born, just because she didn't want to get a dirty look from a doctor. And then after her arrest, she refused to suck it up and deal with her father - resulting in her being out of commission for five years, even though she knew William and Randall were out there. Also, the "she couldn't do anything because she was in prison" excuse doesn't hold, considering that she made no effort to contact William or Randall after she was released.
"She was punishing herself" isn't a very good excuse, either. She didn't just punish herself. She allowed William to think she was dead all those years, and she ignored her son's existence. It would be one thing if she knew that Randall had been adopted by loving parents, but she had no clue if he was living in an orphanage or on the street or what have you. She was a deadbeat mother who ran from everything, despite knowing fully well that her family had money that could transform her child's life if he was living in poverty.