New Zealand Law
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For very young children your present arrangement would be likely to be what is the best plan for parenting. A child this young cannot be left with the other parent in this sitaution until she is much older. So if he does not accept this, then the next step is FDR Family Mediation, where he would need to propose the saftey arrangements and full details. But if the mediation doesnt work, then a Family Court judge will want to ensure the child is safe and probably not allow any unsupervised contact until the child is at least two.
You can encourage him to visit on a supervised basis, and perhaps keep a diary of the times he visits with notes on what he does during the visits.
This would enable you to keep a record of how he performs, and whether he is really serious about contact. Often you will find it is more about trying to cut back his child support liability. But he is unlikely to be able to have joint parenting until the child is a few years older and he has developed a relationship with her