I understand the challenges you are facing, and I am sorry for the situation you find yourself in. Looking at this as a legal issue, you may not like what you're about to hear.
First, the family dispute resolution conference (or mediation) that you're former spouse is trying to organise is a mandatory pre-procedure before either party can apply to the court for parenting orders. It's an opportunity whereby an unbiased third party mediates a meeting between the parents so they can try and negotiate care arrangements for the kids that reflect their best interests. A family dispute resolution conference can be carried out in a number of ways - you can both have legal representation to give you guidance, you can sit in the same room, or you can communicate via telephone shuttle if either party prefers it that way. What is said and discussed in mediation is confidential and can't be used in court.
If the parties reach agreement, they can enter into a parenting plan, which is a formal agreement between the parents, but is not legally binding, meaning the court is unable to do anything if either parent contravenes the agreement. If a parenting plan is made, however, you can then have it made into consent orders, which will give the court jurisdiction to address contraventions if they happen.
If the parties are unable to reach agreement, however, or if one of the parties refuses to attend or does not make a genuine effort to reach agreement, the mediator will issue a S 60I certificate, enabling the parties to file an initiating application for the court to have the parenting matter decided for them.
If the matter were to go to court, the court would determine parenting orders that it deems to be in the best interests of this child. Consideration as to what's in the best interests of the child is provided in section 60CC of the Family Law Act 1975. The primary considerations are the benefit to the child of having a meaningful relationship with both parents, and the need to protect the child from risk of harm caused by neglect, family violence or abuse.
So, what you're talking about in your case is a risk of harm caused by family violence, but as children under section 60B of the Family Law Act 1975 have a legal right to know, spend time and communicate with both parents on a regular basis, the court will go to extraordinary lengths to simultaneously protect the child from that risk whilst also ensuring their rights are upheld. Accomplishing a no-contact order is near on impossible, these days - the court will explore a broad range of options long before it will order that a child have no contact with a parent. It's more likely to order that time between parent and child be supervised, or that the father attend on a psychologist, or that the parents attend a post-separation parenting course, etc.
These are also things you can ask for in your family dispute resolution conference to try and avoid long and arduous court proceedings, as well, but refusing outright to negotiate about the children seeing their father is likely to lead to a hearing. Both you and the father will at all times share equally in parental responsibility, as well, unless the court orders otherwise, meaning you're both equally responsible for making decisions about the long-term care, welfare and development of the children. As such, you're both expected to try and reach agreement about such decisions.
I realise you would have been hoping for a better response, but unfortunately, it would be a lie to suggest that a no-contact order is easily within reach. It's not an easy order to have made, and costs upwards of three years in time, $30,000 in funds and an unknown amount of stress and hardship.
Talk to Relationships Australia about counselling options, not just for you, but also to pitch to the father in family dispute resolution. I believe the Family Relationships Centre also offers contact centres, if you want to talk to them about supervised time between the father and the children.
