Hello Harry,
Another thought is that if you get Jane's English birth cert that will give her mother's maiden name, making it easier to find her parents' marriage cert.
When did Jane arrive in NZ and at what age?
If you post Jane's date and place of birth (which you should be able to get from NZ records - her children's births, her marriage, and her death) someone will be able to help you find her birth in the indexes and explain how to order the cert via the internet.
Sue