You don't have any rights... The kids have the right to have a relationship with both parents.
So I'm thinking things are a bit rocky right now? Are there an conversations around how much access the ex is gonna agree to? So time to get yourself informed about some of the practicalities.
So for example, child support and family tax benefit are based on % of care. If you have less than 35% care you don't get family tax benefit. If you have 36% care you do and you pay less child support and the other parent loses lots of family tax benefit. This is often the reason why one parent tries to minimise the other parent's time with kids
Do mediation - stick to your guns. If you can do 50/50 then go for it. You can accept less at mediation as a provisional parenting plan and let the ex know that you'll accept it only until such time as she agrees to 50/50 or you get a magistrate to agree.
Chances of the ex agreeing to 50/50? don't know ask her. Chances of a magistrate agreeing. Pretty good. Have a read - especially the bit about court data.
Family Matters - Issue 88 - Shared care time | Australian Institute of Family Studies
It is highly unlikely that you'll get to court, but the threat of court often is enough to encourage further compromise...
One more stupid thing you need to know. A parenting plan agreed at mediation is not legally enforceable. So you do mediation make a plan and a week later she changes her mind. Bugger..but the flip side is you can come to a provisional agreement and after that apply for court orders.
Court / consent orders are legally enforceable but they area really hard to get changed... So you wanna get it right.
Final thought - can you get some sort of agreement out of her before she leaves?