I agree with pettygrunder for the most part... However, I think the word "but" is a sticky one... other ways to apologize, that come out naturally for me, when they are sincere, go more along the lines of...
Hey Sis... I was having a really bad day yesterday... blah..blah..blah.. I didn't mean to take it out on you.. I'm sorry. OR
I'm sorry I attacked you yesterday with my words. It was wrong that I took out my personal frustrations on you.
If the apology is received, the dialog usually continues... Thats OK, I'm over it... Is everything alright.. You can talk to me about it if you want...
The door is opened for honest communication.... I'm sorry, but if someone says "I'm sorry, but I was having a bad day" it doesn't come across as sincere at all. --- In other words, do really believe I'm sorry about having this opinion...
gambit
Was this off topic?