Does a parent who had lost custody of his first child for child neglect/neglegence have a chance for custody?

My ex and I are going through a terrible child custody situation here in California. I have NO criminal record what so ever and I have sole legal and physical custody of our children. He and his attorney are lying terribly about me I even had to do a drug test (I chose hair follicle and all was negative of course). My question is this, since he is lying and trying to prevent me from moving, I ran his criminal record. I found out he lost custody of his first child 15 years ago due to child neglect/negligence. He also has a ton of drug charges, battery, theft, and is on probation for DUI and just got another drunk in public. My question is...will his child neglect/endangerment chargers from his first child that is not mine matter in my case? Will that go negatively against him? He could only see his first child after awhile for visitation and it was court ordered that he could only see him if I was around....will any of this matter with my current case? Thank you