Relocation cases are difficult to predict, even in what seems like the most obvious of circumstances, so I'm not going to speculate on what the Court might decide, but the general rule is that if there's no parenting orders, there's no rules that stop you from relocating. Certainly, if you do it without dad's consent, that can cause other problems such as recovery orders being filed, so it's best to get dad's consent first.
Contact Legal Aid or Relationships Australia to organise mediation. If he doesn't participate, then I'd probably consider relocating and letting dad pursue parenting orders, but if he does participate and is opposed, then it might be necessary to go to Court.
Basically, what I've observed of relocation cases is that the Court is more likely to facilitate a relocation application if the applicant parent is likely to facilitate the relationship between the kids and the parent they would be leaving behind, regardless of the distance.
From what you've said so far, I think there are some issues in your approach to the father that would be better addressed now so that, if it does end up going to Court, the father can't make the case the you don't support or encourage the kids' relationship with him and therefore the relocation shouldn't be allowed.
First, even though you're willing to facilitate some limited contact if you relocate, the fact that you are not willing to communicate with dad about major long-term decisions affecting the kids is a problem. Unless you have a Court order stating otherwise, you and dad share equally in parental responsibility, meaning you have an obligation to consult with dad about all major long-term decisions affecting his kids.
Education is very clearly listed in the Family Law Act as one of the major long-term decisions governed by parental responsibility, yet you didn't communicate about which school his children would be attending (but go on to complain that he wouldn't assist with school fees? Come on, now...).
My question is, since you'll be living further away, what other major long-term decisions will you feel yourself at liberty to make without his input? What else won't you communicate about in regards to his kids? Will you discuss counselling options if one of the kids shows signs of a serious personality disorder? Will you advise dad which hospital your kid is attending for surgery after an accident? Or will you only want his input if it's in the form of money?
If you don't think dad is significant enough to talk about school choices with when living in the same area, then why would the Court believe that you consider him significant enough to ensure the kids receive the support and encouragement they need to maintain a relationship with him over distance?
Support and encouragement of the relationship between children and their non-resident parent is crucial in parenting matters, such that it can single-handedly dictate what the Court decides in terms of who the children live with. It doesn't sound like your lack of support and encouragement is maliciously intended, but the passive nature in which you let two five-year-olds decide how long they spend with their dad is somewhat telling - they think candy is an acceptable breakfast choice, so not exactly capable of acting in their own best interests, yet at the moment, you let them decide how long their dad gets to parent them.
Do you plan on letting them stay home every time they say they don't want to go to school? Why is being parented any different? What happens if you relocate and they say they don't want to see dad over the holidays? Are you going to tell dad they don't want to see him, or are you going to do the parent thing and say 'Well, sorry, kids, but that's mine and your father's choice to make, not yours' and send them on their merry way?
On top of that, it's very difficult to reconcile the notion that the father has been inconsistent in their lives, yet now that he's seeing the kids consistently every fortnight for what I understand is meant to be an overnight (but isn't because the kids are currently deciding their own care schedule), you want to make him inconsistent again by moving the kids 4.5 hours away and relegating him to half holidays that may or may not even happen, conditional on the kids approving their time with their own parent.
I also think you're offering an unnecessarily limited amount of time for the kids to spend with their dad off the back of seeing him every second Wednesday. Half holidays is appropriate for parents living flight-distance apart, but a driving distance of 4.5 hours can comfortably enable at least two weekends a term and half holidays.
