You need a small string of legal documents.
1. Your birth certificate, showing your mother's maiden name.
2. Your mother's birth/baptismal certificate, showing her parents' names.
3. Any immigration record that might show location.
4. Any letters from people in CR (or Czechoslovakia or Bohemia or Moravia) that indicate a relationship with Aloisia.
These can then be compared to Aloisia's data. I don't know what happens after that. We too have "one last person" living "in a nursing home somewhere". But our relationship is much more distant than yours.
By the way, today it is the Czech Republic. Before World War I ended it was still Bohemia, Moravia, etc. After WWI and before the takeover, it was Czechoslovakia. Some of the historians can supply exact dates. The historians love it when you get it right. Aloisia was not technically born in Czechoslovakia, because it did not exist yet in 1903.
There are some Czech sites where you can ask for this kind of help. One that comes to mind is myczechrepublic.com