Your girlfriend is upset and moody because you aren't being emotionally responsive to her wishes. She has been missing you for weeks, and she asked you to come home on Saturday, her only free night, so that she could go out with you. You told her that you would be home on Sunday, which wasn't responsive to her request.
Let me tell you a secret about women. In order for your relationship to run smoothly, you need to make your woman feel first in your life; number one on your list; your top priority. When you ignored her request and told her that you would be coming on Sunday, not Saturday, the message she received from you was that your brother and your vacation is more important to you than are her needs and feelings.
I am not saying that a man must always give in to a woman and deny what he needs to do for himself. The goal is to be as responsive as possible, and when you cannot be responsive in actions, then you need to say in words that her needs are important to you and that you would respond if you could.
Here's a favorite example of mine. A couple goes into a jewelry store and the woman sees a beautiful diamond ring. She tells him how much she loves the ring, to which he replies, 'What are you nuts. You think I'm made of money. ' Not a good response even if it's true that the guy is broke! The right response is to talk to the woman's heart, give the feeling that you would say yes if you could.
Responding in an open hearted, emotionally positive way, even though you must say no in action, is the key. Women are moved when they are given the proper emotional response. So, in the jewelry example, the right response would be, 'Honey, that ring was made for your finger. I wish I had the money to buy it for you. When I am more well-off, that 's the ring that you will get. '
Now, back to your case. First, you need to examine why you didn't respond to her wish that you return on Saturday. If it was truly impossible to respond in action (you couldn't change your ticket, for example) then you needed to say, ' I would like nothing better than to be with you on Saturday. I would be there if I could (then give a legitimate reason why you can't).'
Finally, you needed to ask her what you can say or do to make it up to her? It's still not too late to say the above to her. When she feels that your heart is saying 'yes, ' meaning that your words convey that you want to be responsive to her wishes, she will be less bothered if and when you need to say no in actions.
For more information on how to be emotionally responsive to a woman's requests, read my book. This will really set you straight and immunize you against similar fights in the future.