You could not have handled this better. You could not have foreseen your boss's reaction because it was irrational. Since she had never exhibited such irrational behavior before, you could not possibly have anticipated it and developed a strategy to accommodate it.
Please know that you did absolutely nothing wrong. You had a serious problem that even the meanest manager would normally grant you leeway to deal with; there was nothing remotely wrong with asking for time off. You even negotiated with her, meeting her more than halfway, something few people could or would do in the same circumstances.
About the only thing I can think of in order to mount at least a meager defense of your boss is that she might not have believed you about the "sick uncle." A lot of people use the term just like that, with quote marks around it in type so bold that you can see them forming in the air as the words come out of the person's mouth. I know that you weren't lying, but the sick relative excuse has been used as a lie for so long that it's become a comic-strip joke and some people just assume that it's never true.
(The famous sign on the boss's door: To all employees requesting time off for their grandmother's funeral, Please submit your request at least three days before the game.)
I have a hunch that your own boss did believe you, but as I said this is the only thing I can think of that might possibly have gotten you off on the wrong foot. You might want to replay the conversation in your head to make sure that your honesty was self-evident.
Other than that, your boss was just a jerk. Usually this change in attitude toward one person has very little to do with the hapless victim, but is the result of transferring hostility from a relationship in which she has no power into one in which she can vent and get away with it. She might be on shaky ground with her own boss, her husband, her secret boyfriend, her even more secret girlfriend, or some other important person in her life.
You're the victim of bad luck. Life isn't fair, but no matter how many times we say that to each other and to ourselves, it always hurts. I'm sorry for your career loss and also for the personal pain this is causing you. I can't do anything for your career, but I hope that at least I can help you deal with the pain by realizing that none if this was your fault. Don't play "what if" and beat yourself up because you didn't handle it correctly. That just is not what happened.
Don't learn the wrong lesson from this and start being gun-shy and meek and overly solicitous with your next boss. We actually don't like that kind of behavior. ^_^ Be yourself and trust in the law of averages. This won't happen again real soon.
Peace
