If you have a death date why not try to find an obituary. I've had a good response using ask a librarian online. Most libraries have a link to ask a question or some way to contact them. I request an obit look-up and always offer to pay for research, postage and photo copies. Most often there is no charge or a very reasonable charge. I'll bet it mentions when she came, her parents and siblings. Good Luck.
Do you have any data on your grandmother's brother Vito. Birth, Death, Immigration. Could your grandmother traveled with her brother to US? Any info for Vito could bring to the information you want for your grandmother too.
which looks to be born on the correct date. If this is Domenica Maria's brother then these would also be her parents too and the mother of Vito is also Domenica Maria but would need someone to translate to be sure. Hope this helps. Eileen