Your best bet is to consult with a PA attorney if that's where the charges are pending. Try re-posting and using PA as your location.
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Dear I just want everything over?
The incident occurred in Pennsylvania, so you will need to hire a local attorney to communicate your desire to the local prosecutor to withdraw the charges and hopefully your father would agree to request that the case against you is dismissed as well. So if you hire local counsel to defend you (as you cannot defend yourself), your attorney and your father's attorney could work something out to present to the prosecutor to close this sorry incident out.
While your father has not taken to the Internet to confess his participation in an incident that landed both combatants facing charges, only you have gone online in an active criminal matter in a public forum. You may have just provided the information the prosecutor would need to drop the charges against your father and go after you alone.
In a criminal prosecution an admission against interest could be turned into evidence to prove a case. Hire an attorney and stop discussing this matter in public or anywhere where you are not protected by confidentiality.
Stay safe and silent.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.
Interpersonal relations are criminalized across the country. So if you admitted to kicking him, you are now charged with assault. He choked you so he is charged with criminal obstruction of an airway, or whatever Pennsylvania calls it in their criminal code. These federal laws are masked by state nomenclature to give the appearance of state dominion. For example, Pennsylvania has the Protection From Abuse Act 23 Pa. C.S.A. §6102 which is a copy of similar acts across the U.S.
In Pennsylvania, arrests take place at the officer's discretion. 18 Pa. Cons. Stat. Ann. § 2711. However, it appears in your case, given two federal matching fund payments for the price of one, the officer arrested you both. 18 Pa.C.S.A. §2711: Probable Cause Arrests in Domestic Violence Cases. Then comes prosecution.
Prosecution is "no drop" which means after a year in the adjournment part, you'll face trial. Or, if the prosecutor takes no action on your case, you'll move to dismiss the matter on speedy trial grounds. However, given the facts of your case, you have a catch 22. You cannot withdraw your complaint against the father because you assaulted him, and he cannot drop his prosecution because he choked you. So you are locked in a procedural embrace you cannot get out of unless you go to trial and both refuse to testify against each other, and even still, the prosecutor can proceed with his case just using the police report as proof. This is indeed the outcome in every domestic violence case.
This law was brought to you by legislators who reviewed studies of people violenced domestically. They found that victims are prone to suffer more violence if they can withdraw their cases themselves. So to protect violenced individuals, no-drop prosecutions are now the law. So one size fits all and welcome to ranks of the criminally convicted. To prevent this from happening again, be lady-like and ask dad to be a perfect gentleman.