There is a presumption that both parents have shared parental responsibility for their children, which means they both have a say about their living and care arrangements. While ever there are no orders or parenting plans in place, there is nothing to restrict the mother from moving without your consent, but if she does so, you can apply for a recovery order, which would likely be accompanied by an application for parenting orders as well.
The usual process is to first attend mediation to discuss the matter and try and reach an agreement as a section 60i certificate is in most cases required before proceedings can commence in court. However, it may be bypassed if the application is urgent. This might be the case if the mother moves without your consent before mediation or before proceedings can commence.
If you happen to apply for a relocation order and parenting orders, you can also seek interim orders that place an injunction on the mother to stop her from relocating.
For added information, parenting orders are made to meet the best interests of the children, and what the court takes into consideration is the benefit to the children of having a relationship with both parents, the need to protect them from harm, and a series of secondary considerations, all of which are listed under Section 60CC of the Family Law Act.
If it happened to end up in court, you have many things in your favour.
First, I assume that since only the oldest is in school, the children are quite young and the court recognises that the younger the child, the more regular the contact must be to ensure they can maintain the relationship with both parents. Tyearanny of distance would make that difficult.
Second, you both have family in your current town. The children have a right to also know, spend time and communicate with their extended family on a regular basis.
Third, having a boyfriend of two months in Sydney won't be enough for her to argue that it's in their best interests to be moved from their current home and school to relocate away from the current location.
But, first, contact Legal Aid to start organising a family dispute resolution conference. That at least gets things moving, and if she relocates before FDR takes place, then you'll have grounds to seek an urgent recovery order.
