I don't know all details but from my own experience i'd always suggest to move out.
Being self depend is not only a great way to grow into physical and mental adulthood, but should also improve your relationship with your parents.
On the other hand you don't seem to have a job, so you definitely should focus on that first, because you can't achieve the above mentioned points if you don't have the financial independence.
Why did you ask them for the job search?