Trouble at work?

I have a question about my current nanny position with a family.

To give you the run down. I am a full-time college student at ut. I just moved from Chicago so having a job right away was exciting. When I talked to this family on the phone, they seemed super energetic and happy for me to help out. They knew I was a full-time student, so I needed a flexible schedule. I started three weeks ago, and so far there have been many issues.

Right off the bat, these parents disregarded my wishes. I had just arrived in Austin after driving from Chicago. They wanted me to come three days after I arrived, but I told the father I would feel more comfortable coming at the end of the week because I have a senior dog, I had a lot of stuff to unpack, and I wanted to get settled in before meeting them. They didn’t seem to care about that situation, so I went ahead and went that day.

The following situation was me informing them that I might not be able to watch their child on a particular Thursday due to me having to go to school.
The father's automatic response was, “Well, it better not be the time and day we need you.” I let it go until I could find the exact time I needed to be at school, and I brought it up again the next time I saw them, which would’ve been a two weeks notice. When I brought it up again, I informed them that I had to be at school early in the morning till late evening and would not be able to come that Thursday. His instant response was reasonable to a certain extent. He seemed very angry/ annoyed that I couldn’t watch his child because he didn’t want to call off work and had no one else to watch him. He kept asking me if I was sure I had to be there even though I explained to him that I needed to be. The mother was in the room but didn’t say anything about the situation. Overall I was trying to explain that I was sorry, but he told me they didn’t need me anymore and told me to leave for the night. That was the end of that topic.
Trouble at work?
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