If the offense happened more than a year ago, then you are beyond the statute of limitations for bringing a charge for a misdemeanor. That's the first point.
Second, you should have been charged with domestic assault, not simple assault. The former is the preferred charge because it allows for alternate dispositions rather than a guilty finding, if it comes to that.
The downside to that gets to your final question, can your parents drop the charges? If it is indeed a simple assault, then the prosecutor's office is likely not involved and the complainant (your father) can drop the charges. If it is a domestic assault, there will be a prosecutor who has to drop the charges.
Now let's talk about your defenses. Firstly, a parent has the right in Virginia to mete out punishment to their minor children (you did not indicate your age), including corporal punishment. This would not include punching their child in the mouth, however. If he punched you and then grabbed a hold of your shirt, I would say that you were within your right to exercise self-defense to repel further assault.
Assault & battery is a misdemeanor punishable by up to 12 months in jail. Talk to a criminal lawyer in your area about the charges and the facts of your case. It looks like you may have some viable defenses to the charges.
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Mr. Garrett gave some great advice. You should consider following it.
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Meet with local counsel and discuss whether it would be possible to file a cross charge against your father and what the pros and cons of doing so would be. I don't practice in Woodbridge and wouldn't be comfortable giving you advice about cross charges there, because the local practices and procedures may be different in Woodbridge than Virginia Beach. Since this event happened about a year ago, this conversation needs to take place very quickly. You may be able to file charges against your father, that may increase the likelihood of both cases being dismissed, it may have an impact on whether the Commonwealth's Attorney continues to prosecute the case against you. It might be better to be cast in the light of the victim and a defendant than simply in the the light of a defendant claiming self defense. Nevertheless, there may be unintended consequences to filing cross charges, local procedures may not put you better position, and you may already be time barred from filing a cross charge. Discuss these issues with a local criminal defense attorney.
The information provided herein is intended solely for educational purposes and does not create an attorney-client relationship. Please contact a local attorney for assistance with your matter.