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Dealing with CPS is always difficult. Depending on the case worker assigned to your case it can be manageable or an absolute nightmare.
I always advise clients to remove elements that CPS critiques from the equation if possible. Ie if CPS has an issue with father's girlfriend in addition to father because of allegations of drug use, I would strongly advise that father remove girlfriend from the equation either by separation or moving out of the same living area. Father may have to make a choice between his children vs girlfriend. While they're separated girlfriend can get help or prove that there is no drug issue and then reunite at a later date.
In regards ***** ***** against father directly because of criminal history, I would recommend that father voluntarily attend anger management counseling, parenting classes, and a drug screening showing he is clean. You want to establish for the judge that there are no safety issues for the children in father's custody. Since there's an allegation and a charge of domestic violence you need to establish that any anger management issues are controlled with appropriate counseling, there are no drug issues for father and he has all basic parenting skills. Lastly father has also removed girlfriend from equation.
You have to remember that a parent's number one job is to protect their children from any and all dangers. This includes dangers from yourself, from the other parent, or significant others such as a girlfriend. I have seen many people lose custody not because they themselves have a problem but because of who they live with. It may not be fair but if you're asking me the best way and best chance of reuniting father with children this would be my advice.