Hey Sarah,
From here
https://www.ica.gov.sg/reside/LTVP/apply ,
we can know that you can apply LTVP if you are:
1. Spouse of a Singapore citizen (SC)
2. Spouse of a Singapore permanent resident (PR)
3. Child (aged under 21) of a Singapore citizen (SC) or Singapore permanent resident (PR)
4. Parent of a Singapore citizen (SC) or Singapore permanent resident (PR)
6. Graduate from an Institute of Higher Learning seeking employment in Singapore
7. Mother or Grandmother of a child or grandchild studying in Singapore on a Student’s Pass
8. Visitor seeking permission to give birth in Singapore
and from I get from your case: PR (your father) can be your sponsor for point 2, 3, 4, or 7.
In your case, you are included in
- point 3 (though you are not under 21 y.o)
- point 6 (though you are not from IHLs)
- point 7 (though you are missing some documents and the terms for this point do not meet your purpose for job seeking)
In my mind, idk to apply for LTVP whether ICA will take only 1 "fulfilled point" from these points OR they will consider some "unfulfiled points" (which are you are in) to take into consideration later when u apply. It's like, yes you are a foreign child of a PR (but above 21 yo) that will graduate from SG (but not from a IHLs) and also a mother of a grandchild of a PR which is your own father (you 3 are family members but lack the requirements). Perhaps, I'd be pretty confused to take decision if I were an ICA worker

, no offense but like everyone says, this is pretty unique case and maybe only ICA can answer