Beyond merely apologizing, I'm wondering if you sat down with them and had a talk on why you reacted the way you did. If you've talked to them about feeling that they were over reacting, which maybe was embarrassing you in front of your friends? When you do talk to them, word yourself carefully. I recently posted a response to someone on
how to broach others without offending them and perhaps taking a look at that list will give you a good idea on how to actually express your thoughts and concerns when you talk to your parents.
Don't only express yourself, but ask pointed questions. Things like "I really want to understand what happened and I'm having trouble comprehending why you reacted the way that you did, can you explain it to me please?" This might give you some really good insights into why your father was behaving that way. You could also expand on things by asking phrases like "why do you think that is?" or "how did you feel about-" or "how can we move forward from here?" or "so how do you think we can communicate through something like this better in the future so neither of us suffers any embarrassment [or whatever the feelings are] and this doesn't happen again?" You can add in that you don't believe that your father meant to upset you and that you had not really meant to upset him, you were just [express feelings here] and over reacted yourself and now you understand that he felt [whatever] and why he reacted that way, although you would really like it if you worked together to find a better way of handling these feelings and this kind of situation in the future.
They might be honestly surprised to hear you talk like that if you don't normally, but I will tell you this... those kinds of questions are designed deliberately to elicit more than a one worded response, to get at feelings and to cause thoughts. Sometimes we serve ourselves better by thinking through the situation more, why, what, how, etc and articulating that. It's also a more adult way of working through a situation. I think the fact that you acknowledged that you were rude, is a huge thing for a young person. If you can't deal with your parents right now because of a time crunch on your work, then take a few deep, calming breathes, relax a little, and focus on the task at hand. Then when you're done, go to your parents and ask if they have time to talk for a few minutes about what happened. I wish you the best of luck in all that you do. Take care of you.
