That would depend on the facts and how long ago it happened. But it is a good start, but having an attorney by your side might make it happen as many judges now do not listen to well to pro per litigants especially if they get to emotional. The attorney can play the bad cop while you play the good cop. I would recommend hiring experienced counsel.
My name is Stephen R. Cohen and have practiced since 1974. I practice in Los Angeles and Orange County, CA. These answers do not create an attorney client relationship. My answers may offend I believe in telling the truth, I use common sense as well as the law. Other state's laws may differ.. There are a lot of really good attorneys on this site, I will do limited appearances which are preparation of court documents it is , less expensive. However generally I believe an attorney is better than none, but many will offer a free consultation and a face to face meeting generally will be better, I like my clients to write a short one page history of the fact and questions they have prior to meeting with them, so nothing is forgotten.
A judge, when determining custody issues, will consider the Health, Safety, and General Welfare of the child. The restraining order may be issued if a judge is convinced that the child is unsafe in the presence of the female. Sounds like you have a great shot. Are the negative things you referenced above recent?
The environment in which the children will live is important in determining custody.
However, you asked about a restraining order. For a restraining order to be granted, the court must have evidence of some sort of harm that the children have suffered. The partner's background could be relevant in this context if the children have been abused in some way. The partner's background alone is not enough for you to obtain a domestic violence restraining order.
If you have further questions, see an attorney or go to a legal aid organization if you can't afford one. Good luck!
This is a general information answer ONLY and does NOT create an attorney-client relationship. Without detailed facts about your case, I cannot provide specific legal advice and this answer is not intended to be taken as legal advice.