Okay, so an unfortunate reality check for you is that even the children of meth addicts have a legal right to a meaningful relationship with their parents. The children of alcoholics are no different.
You've asked if your word is enough to guarantee supervised time, but there's a few layers to this question that I think should be addressed.
First, while ever there are no parenting orders in place, you and the kids' father are at liberty to do as you see fit in regard to the children. If you want to hide them away, you can. If he wants to pick them up from school early one day and move across the country with them, he can. The only way you can really protect the children from such games is to get parenting orders.
That brings me to my second point. Parenting orders are made in one of two ways - by consent between the parents, or by order of the Court. The first step in getting parenting orders is to attend a family dispute resolution conference with your ex to try and negotiate an agreement that can be turned into consent orders, or failing that, you receive the s 60I certificate that is a mandatory component of filing an initiating application for parenting orders to be determined by the Court.
Third point, if you ask the Court to decide, it is bound by the Family Law Act, which states that the children's best interests are paramount. When considering what's in the best interests of the children, the Court refers to s 60CC of the Family Law Act 1975. The two primary considerations are the benefit to the children of having a meaningful relationship with both parents, and the need to protect the children from harm caused by neglect, abuse or family violence. There are about 12 secondary considerations, as well.
So, where does alcoholism fit into all of this? How might the Court take the allegation into account?
Well, as a precautionary measure at an interim hearing hearing (parenting matters occur over a very long time with multiple interim hearings before heading to trial), then the Court might order that the father spend supervised time with the children under the watch of a family member or at a contact centre.
If that goes well, it might later order that future time occur without supervision, but an injunction might be issued against alcohol consumption before and during the children's time with him.
If it doesn't go well, the Court might retain supervised time and order the father to undertake rehabilitation. It might move to unsupervised time in future, if the father proves responsive to treatment.
If it can't make a final conclusion, it might order that a family report be completed to provide some third-party insight about how the allegations have affected, or might affect the children's relationship with their dad.
Or the Court might not agree that the allegations of alcoholism are persuasive and just order time to be unsupervised from the beginning.
It's impossible to predict what the Court would do, if it even ends up in Court, but you should prepare yourself for the very real possibility that unsupervised time between the children and their father will take place at some point in the future. It's very uncommon for the Court to order supervised time on a long-term basis, particularly if one party is banking just on their word as evidence.
My stepdaughter's mother once tried to persuade me that my now-husband was suffering from an alcohol addiction, but now that I've been married to him for several years, it's become clear to me that her definition of an alcohol addiction was very different to my own, and thankfully, that's why the Court doesn't take the word of people like you and me as gospel when it comes to medical diagnoses - all we can provide are opinions, not facts. I daresay we wouldn't have gained 50/50 care of my stepdaughter had the Court given weight to the ex's opinion in our case.
All you can do in an affidavit is raise your concerns and cite the pathways you've taken to try and have the issues addressed. That doesn't mean the Court will oblige any wish for supervised time, but it will at least take it into consideration and determine of its own accord if an expert witness needs to be appointed for a proper assessment.