If there are no orders in place, he is able to take the children overseas if both parties have already consented to the acquisition of their passports.
It is true that he can pursue parenting orders through the court to enable them to travel. Likewise, you are within your right to contest it. It's impossible to predict which way the court would rule on something like this, but he sounds like he is a reasonable person if he not intending to travel without either your consent or the consent of the court. If he intended not to return the kids, why pursue consent at all? Kids are ordinarily only stopped from travelling where the circumstances strongly indicate the children would not be returned, and a lack of trust isn't really a good enough reason.
You continue to discuss 'your rights' and 'his rights' and I just want to clarify that neither you, nor the father, have any rights whatsoever under the Family Law Act 1975. Only your daughters have rights that the court will uphold, and those rights are to know, spend time and communicate with both parents and other people relevant to their care on a regular basis, regardless of the nature of relationship between their parents.
You've said the father has had limited involvement, but it sounds like he may want to have more involvement than you have allowed. I think you should know that if the father pursues parenting orders permitting travel, it's likely he will pursue parenting orders for all other matters, and it will look bad for you if you're not seen to encourage and support the relationship between the children and their father. Remember, your daughters love their dad, even if you don't.
