I am in South Australia. I had problems getting a copy of my mother's Death Certificate (I did have a photocopy of it that I had obtained via the Registrar - long story) I am an only child and my father remarried. I ended up taking in my birth and marriage certificate and was granted permission to get my mum's death certificate.
I then had to get my Nanna and Aunt's death certificates. My grandparents raised me (as my mum died when I was 6 weeks old). For reasons unknown I was not named as the person who had identified Registrar of Death (I was not next of kin as my grandfather had been alive, plus her two daughters). Although Nanna was my legal guardian there was no paperwork I could find. They ended up taking the fact that all of the expenses for her funeral and burial were addressed to me as well as a Coroners letter.
My Aunt had no children and although her younger sister was still alive I had been responsible for her but unfortunately due to her mental illness did not have Power of Attorney. Again, because I had letters from the Nursing Home, Funeral Director etc I was able to obtain a copy of her death certificate.
Although I physically have the Deed for my Mother's burial plot I have no rights for it. My father (who doesn't speak to me is her next of kin) When he dies unless he leaves the Deed to me in his will (which he won't and quite frankly I don't think it would be something he would even think about after almost 60 years) it will revert to either my stepmother OR my half brother if my step mother pre deceases my father! So despite the fact that I am my mothers only child under current SA law I have no rights. Thankfully, a few years ago the Cemetery were quite happy to take large amounts of money from me to have the lease on the grave extended.
Good luck! Just get as much documentation to prove who you are and your relationships as you can and good luck. If you can go in there in person it will be all the better.
Deanne