What do you do about not approved vacation time off?

I was hired a month ago for a position I was dying for. I was so happy when I got it. (It took them 2 months to bring me aboard) I have an important court hearing(custody case) in August that I need to attend to and I have a family trip coming up in October. I put in my requests for the days I needed off on Tuesday. I knew my August day off would be an issue because it is so close plus I was on a 90 day probation period. I was pulled in the office yesterday and was told because I was new she would not grant me the time off, I explained to her I can not miss my court date and my family trip was already preplanned and could not be cancelled. I also advised her that the trip was 4 months away and not during my probation period, my boss then told me she still could not approve it. I have never worked for a company that didn't approved time off (paid or not) especially when it is done in so much in advance, some people told me I should have waited to request the time off but I didn't want to wait a month prior especially if I know now. I only found out that about the court date two weeks ago. She asked me why I didn't mention it in the interview I told her we interviewed in April I had no idea that no.1 it was going to take 2 months to bring me aboard (when I would follow up after my interview they kept pushing back the hire date each week every time I called they would say next week) and that no. 2 an event in October would be an issue since the date is so far away and that I did not know about the court date until two weeks ago. She told me she would grant me the time off the court date since it was court but she didn't want to, After she said that I told her I had to resign. She said it was my choice and I said no you are making it my choice. She said she also had an issue with me coming in 15 minutes earlier than scheduled, I just walked out. I was not going into coming in earlier than scheduled I thought that was a good thing. I didn't understand why she wouldn't approve the time off even though it was after my probation period. How do one handle not getting time approved off at a job and being too punctual?