and your boss is a micromanager, if one of my staff wants to leave early for some reason, i wouldn't mind as long as she/he has a good track record with me.
I'd recommend that you explain your situation to her in person, for example, that you have to send your cat to your friend's house or pet daycare at certain time, plus you have to pack for the trip....I get a feelig that she won't understand anyways, but it's your responsibility to do so.
next time, either recommend a later flight or maybe someone else can go instead of you.