Legal Question in Criminal Law in California

You're on the right track. What is "in the interests of justice' is completely up for interpretation by the judge. You need to show proof that 1) you have learned your lesson or whatever it was that led to the underlying conviction has been addressed and remedied, and this is something that will never happen again, 2) that the conviction is the reason you are unable to find employment, and 3) without employment the children are suffering. I would get letters of recommendation from people who know you well and can speak highly of you as a parent, preferably from someone like a pastor at your church or other such respected persons. Show your qualifications to get a good job, such as a college or other professional degree or training, that but for the conviction you would receive the job. I would recommend you at least speak (in person) with an attorney about filing a 1203.3 motion, as it is rarely done in pro per, but it sounds like you grasp the concept enough to give it a try on your own. If you'd like to contact me (find me on Google) I may be able to send you in the right direction. Good luck.

You'll state and rely upon whatever arguments you've got. The decision is up to the judge. If serious about hiring counsel to help in this, feel free to contact me.