Mm, most free dispute resolution services have very long wait times. The last time we used one, we started the process in July and didn't actually mediate until the following February. Lucky for us, though, we already had sealed orders, so the wait time wasn't at the expense of the child involved.
The professionals are correct - such a lengthy separation is not in the children's best interests, and god willing, mum will get the same advice from a lawyer, too. The Court doesn't take well to parents who needlessly stop their kids from having a relationship with the other parent, but it's often a lawyer who has to explain this to the offending parent.
For now, though, there isn't a great deal that you can do, except maybe arm yourself with knowledge. While there are no orders in place, parents can do as they see fit, but it's important to be patient and remain calm (and seek support if you need) so your words or actions aren't at risk of creating problems down the line (like a heat-of-the-moment text message being brought up as threatening behaviour by the other parent in future proceedings). It's critical to remain reasonable and amicable at all times so you never fall into the trap of giving mum ammunition, should it end up in Court.
My suggestion is to write to your ex politely requesting time with the kids - "Hi, I was wondering if the kids are available to spend time with me on [date]? I am happy to collect them at [time] and return them at [time] the following day. Please let me know if this works for you, or otherwise advise of a time and date which suits you better." If mum says no, simply say, "Okay, no problem, if there is another day that works for you, please let me know." Wait a week or two and then ask again.
The reason I suggest this is because you'll be developing a track record of being flexible and showing your efforts to see the kids, and she will either work together with you on that which benefits the kids, or she will be developing a track record of rigid refusal to facilitate the kids' relationship with you.
For mediation, come to the table with a proposal for what kind of time you think the kids should spend with each of you. Given the kids are all fairly similar in age, it's probably appropriate to expect that they stay on the same schedule, but as they are also very young, you shouldn't expect them to move to a 50/50 arrangement immediately. For young children, it's often the case that kids cope better with shorter visits more frequently, rather than longer visits less frequently. For example, one or two overnights in a row will be better for the kids than five or six overnights in a row, at least until they get older.
There are some concerning features in your case, like not knowing where the kids live. It's a standard clause in parenting orders for parents to keep each other informed of contact information, so include this as an issue to raise in mediation. You might also consider seeking a clause that limits either parent from relocating with the children to another town without the other parent's agreement.
In the event mediation fails (and it usually does, unfortunately, but you should go into it hoping that it doesn't), then you'll be granted a s60I certificate, which forms a mandatory document to be filed with an initiating application for parenting orders from the Family Court. If mum has refused to disclose her address at mediation, you would need to seek a location order from the Court, as well.
I hate to say this, but in my experience, level-headed fathers nearly always get a better deal from the Courts than what they can get through mediation with the ex, and you can blame decades of ill-informed societal support for dads only seeing their kids every other weekend for that.
Modern Australian legislation, in contrast, heavily supports shared parenting in this country - equal shared parental responsibility is a presumption, which means the only time it isn't ordered is if someone successfully rebuts it (uncommon), and where that presumption is upheld, the Court has to consider if equal time is in the best interests of the kids first, and failing that, it has to consider substantial and significant time as the next best thing. Substantial and significant time is a combination of weekends, weekdays, holidays and special occasions, so every-other-weekend is very much the exception, rather than the rule. I'd say the average outcome in a case with no mitigating features is five nights a fortnight, if not more.
For added interest, about 95% of parenting matters initiated in Court are later settled by consent. Only about 5% are actually determined at trial. Trial is the most expensive part of the whole process, so if your ex is paying for her own lawyer, she's got good motivation to settle. If she's funded, Legal Aid very rarely funds matters at trial, so again, good motivation to settle. The prospect of $20,000+ in legal fees can make even the most determined ex reconsider their position.
If I may, what reason has she given for withholding the kids, and for not disclosing their current address?