Should she stop her prayer because her family does not know that she is Muslim?

No File Exists
Check below answers in case you are looking for other related questions:
Ruling on making du’aa’ in languages other than Arabic in the prayer
Should she leave the prayer in congregation because her child cries?

No File Exists
Related Answers:
Stopping one’s prayer in cases of necessity
Should he interrupt his prayer in order to answer one of his parents if they call him?
What should a non-Arab do for the adhkaar in salaah?
Ruling on making du’aa’ in languages other than Arabic in the prayer
Should she leave the prayer in congregation because her child cries?

Recommended answers for you:
Celebrating the night of the Isra’ and Mi’raaj
Being Successful in Life
Problem between a daughter and her mother
What is the ruling on a man having intercourse with his pregnant wife?
Obeying one’s husband comes before obeying one’s parents and siblings