Can my employer ask about the details of my family emergency?

Question Details: I went home early from work and told my employer that I needed to leave due to a family emergency. My employer was very upset with me and asked, "Well what is your family emergency? Why do you need to leave?" And basically she told me that she was going to decide if it was a good enough reason for me to leave work. She allowed me to leave but told me that I had an obligation to my employer and that in the future if I wanted to continue working there, I would need to choose between family and work. Is she allowed to ask specific details like that? Is she allowed to tell me to chose between family and work legally?

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