The practising lawyers here will likely tell you that you can apply for sole parental responsibility and a no contact order against the other parent, no problem, and if you want to take that advice, there's nothing stopping you from doing so.
What they won't tell you at that first consultation is that you're looking at two to three years in Court, upwards of $30,000 to cover their fees, and at the end of it all, a very, very low likelihood of success because the legislation does not favour kids growing up in sole parent families, which means you'll probably end up settling by consent at that point anyway, and you'll be wondering why you wasted all that time and money on a lawyer in the first place.
What you get from this forum, on the other hand, isn't legal advice. It's guidance on the law and the process from individuals who have knowledge about the law and the process, gained directly from our own experiences in the Courtroom, and on top of that, we also have absolutely nothing to gain from your case.
A lawyer will tell you what can happen in theory. We will tell you what we think is more likely to happen in reality. It's entirely up to you which view you choose to give weight to.
So, on that premise, my view.
Paramount to the Court's concern is the best interests of the kids, and what the Court takes into consideration when determining the best interests of the kids is listed in s 60CC of the Family Law Act. Among those is the benefit to the children of having a meaningful relationship with both parents; and also the need to protect them from harm caused by abuse, neglect or violence.
At a State law level, abuse is fairly broad in its definition, but the Family Court has a higher threshold for what kind of behaviours it considers to prove an unacceptable risk of harm to the children, such that a no contact order is in their best interests. If there are no police reports, investigations, charges or convictions, no IVOs made after a finding of fact that violence has occurred, no convicted breaches of an IVO, and no reports to DOCS about child abuse, then the only proof you have at this point to show there's an unacceptable risk of harm to the kids if they spend time with their father is your word against his.
The legislation favours children's rights, which are to know, spend time and communicate with both parents on a regular basis, regardless of whether they are married, separated, divorced, de facto or have never been in a domestic relationship at all. When you ask the Court to make an order for sole parental responsibility, you are asking the Court to make an order that undoes those legislated rights, which is not something the Court takes lightly. Shared parental responsibility is a presumption under law, which means it can only be removed by an order from the Court, after it has been successfully rebutted by showing shared parental responsibility is not in the best interests of the kids. That might sound easy enough, but since shared parental responsibility is a presumption under law, the burden would be upon you to argue why you're right, rather than upon the father to argue why you're wrong.
As an analogy, imagine having to persuade a liberal to vote labor.
Orders for what time a child spends with each parent goes largely hand in hand with the legislative preference for shared parental responsibility. If the presumption of shared parental responsibility is not successfully rebutted, the Court must consider if equal care is in the best interests of the kids, and failing that, it must then consider if substantial and significant time is the next best thing. Substantial and significant time is a combination of weekdays, weekends, holiday time and special occasions.
Of course, consideration for equal time or other doesn't mean the Court must rule either equal time or other, just that it must consider it.
The final point I want to make is that even though this isn't explicitly legislated anymore, the Court also considers the capacity of each parent to support and encourage the child's relationship with the other parent, under the 'other relevant issues' part of s 60CC. The Court doesn't take well to parents who are unable to put their personal issues aside and recognise that both parents have an important part to play in their kids' lives. More than once, I have seen cases where the Court even reversed residency arrangements because one parent has worked so hard to stop the other from being involved in their kids' lives, contrary to the kids' best interests.
My view is that the complaints here appear to be fairly low key, as far as violence and abuse goes by Family Court standards. An IVO doesn't have a great deal of weight behind it if there's been no police action on it and it was accepted without admissions. Parents with IVOs have been granted residency before. Gambling and drinking doesn't an unfit parent make, either. At best, the Court might order he consume no alcohol before and during the kids' time with him. The complaint about non-involvement is fairly menial. If dad is still seeing the kids, or even expressing interest in seeing the kids (which one would assume he is, since it sounds like he's commenced action to do so) then the Court is probably going to see it best that the kids spend time with him and benefit from his continued involvement.
Basically, I don't think you'll get sole parental responsibility and a no contact order in your favour, but nobody can ever predict what the Court will order, so I could be wrong. It's really up to you how you proceed.