He tried to leave in chapter 45 to study abroad but Jesse stopped him. But yeah it's true that his mother told him that he could leave Jesse but he objected every time.
Jesse didnt stop him. Jesse didnt want law to go but law deep down knew he couldnt leave and jesse wouldnt want him to leave. it was part of his plan to manipulate jesse.
It's true in chapter 43 he only said that he would follow his parents decision to see Jesse's reaction but in chapter 45 we see him seriously considering leaving Jesse to get his act together . And that's when Jesse called him and attempted to stop him.
Law has problems honestly. Law wants to control everything about jesse even his MIND! I thought jesse was obssesive but its law who is obssesive and CRAZY LIKE HOLY SHIT. law has fcked up shit going on in his mind to do this to jesse. He wants to manipulate and control jesse and he wants to be free or 'equal' as he says but like law could have left jesse ages ago but he still stayed and is saying he is being controlled. Jesse can live without law but law is the one who cant.