You don't have to prove anything. The prosecution has to prove that you are guilty, beyond a reasonable doubt. Don't tell the police anything except your name and that you deny the charges. If you can't afford a private attorney, use the public defender; they know their job, they just have too many clients. Your lawyer may be able to cut you a deal. If you go to trial, look your best. Listen to the questions carefully, and then answer them, briefly and to the point. Stay calm, and speak up, so everybody can hear you. Be sure to demand a jury trial and look the jurors in the eye when you tell them you are innocent. The prosecution needs to convince everybody on the jury that you are guilty, but on almost every urban jury, you can count on having somebody who has had a bad experience with the police; don't think everybody on the jury is against you, and you only need to get one juror on your side. Good luck -- and stay out of trouble! PLEASE READ: I am not your attorney. No attorney-client relationship is created between you and me by you posting your question on AVVO and me answering it. My analysis is based on the limited facts available to me; you should get your own lawyer and take that lawyer's advice after he or she has all the facts.
What does "insistent" mean to you? None of the usual meanings of insistent seems to apply here.
If you used the wrong terms in your statements to the police, you may have left the officers with the wrong impressions of what happened.
Police officers do not have to answer any questions to the person being arrested while the arrest is happening.
It is not unusual that some factual assertions on police reports are incorrect.
What you should do is review your specific facts with your attorney. If you are low income by local standards, you are eligible for representation by a public defender who is an attorney paid by the city or county. The court hearing your case should have information on what you need to do to apply for a public defender.
You should not disclose the details of your case to anyone but your attorney. Other persons may not have any privilege to assert to not testify to what you tell the persons. In WA, there generally is no spousal immunity in domestic violence cases.