As the victim, what would the proper way to write a letter requesting a "nolle prossed" in a domestic violence case?

You can file a request to not prosecute. The standard forms are at the State Attorney's office. You can also tell the prosecutor in person at the invest. Good luck.

there is a form provided by some state attorney offices which you can use. there is no magic language, however, in my experience any attempt by you to make the authorities look bad will not be welcomed. your honest explanation of what happened and how it was provoked by your behavior will be appreciated by the state attorney and may be taken into consideration in making a charging decision. you really should use the "find a lawyer" function on this website to find an experienced criminal defense attorney in the jurisdiction where he is to be charged and ask for a free initial consultation. he or she may be able to give you some more specific advise and may be willing to assist you for a reasonable fee. good luck.

In my experience, they SAO tends to ignore victim requests to drop charges in DV cases. The reluctance to drop cases stems from fear of future violence.