Your first step is to find out her exact date of death. You can do this from the tombstone, or from a death index or obituary index.
Then you should obtain, for your own records, a copy of her death certificate and obituary. The death certificate can be gotten from that state's Department of Vital
Records or it might be called the Department of Health. The obituary can be obtained from the library in the town/county where she died, from their newspapers on microfilm.
These two documents can answer a lot of questions and pinpoint a lot of details that you do not yet have.
Once you have those, it will then be easier to find her siblings and parents.