My mother recently passed and a mass is being held for her on Saturday. Is it possible to enter St. Jude's Church this Saturday morning to pray on my own and be with her in spirit?

It depends on what time you go.

St. Jude is not open on Saturday mornings, but i know that St. Mary Catholic Church (next to the library) is open at 8am because they have a Mass.

You will have to call the church to find out when the sanctuary is open. My condolences on your mother's passing.