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Can the mother take my 14 year old to live in Canada without my consent

Hi All,
I live in Australia but the mother of my children lives in NZ and is in custody of 2 of my children. Recently she has applied to the Family Court to take my 14 year old daughter to Canada whilst at the same time trying to have my guardian rights removed so I won’t have a say in the matter.

I am currently waiting to hear what the Court has to say about my application for variation of parenting order which I’m doing in an effort to get my daughter to visit me in Oz during school holidays. That’s a separate issue however and I haven’t received a hearing date or any feedback from the Court yet. She has told the Court that she has to move to Canada because she sees no future for her or my daughter in NZ. That’s total BS really but I won’t go into that because it’s a long story.

The mother was born in Canada so can claim Canadian citizenship and I believe the kids inherit this status. There is to be a review re her application in 2 weeks and the Court will then decide to proceed with it. I have a good record as far as the Court is concerned so it’s not as though I am an abusive parent/ex spouse or anything like that. So, the main thing I need to know is can she do this without my consent or will she get blocked at the airport if she tries it,and would the FC just tell her it’s a no go anyway ? My main objections are that she is an incompetent parent (lots of proof re this from CYF, MOE etc) and that if she is taken to Canada she will probably go to ground and I will never see my daughter again. Any ideas???