Any domestic violence offense is very bad news for immigration consequences. You should absolutely not accept any plea deal until you consult with an attorney. I would suggest starting with the Washington Defender Association - http://www.defensenet.org/immigration-project/immigration
It would probably be in your best interests to hire an attorney who practices criminal defense regularly in the court where your charge is filed, and that person will be able to give you more complete and reliable answers. However, I can tell you that in my experience in criminal defense it would be highly unusual for a person in your situation to receive any jail time, and in many cases like yours it will often be possible to enter an agreement with the prosecutor to perform community service...
Most police departments have a public information office, where citizens can request public disclosure of police reports and sometimes 911 call recordings as well. I suggest that you call the police agency that was involved and they should be able to help you request the documents - there is usually a form. Most states have rules allowing government agencies 5-10 days to respond to public disclosure requests. Likely you can get the reports within a total of two weeks, if not faster.
Your case must be for more than a speeding ticket, or you would not have an arrest warrant. I recommend taking all of the information you have showing your attempts to get to court and attend the hearing to request that the judge cancel the arrest warrant. Waiting will only make it worse. You will need an attorney.
In general, issues of police brutality have little impact on criminal cases. The Miranda rule is only relevant if you made statements under in-custody interrogation without the warnings; in that case the statements would be thrown out, but the case would not be dismissed unless the State cannot prove its case without the statements.
It may be that you have a separate civil rights claim, I recommend consulting an attorney.
It will be difficult to pursue this claim because you will have to show that your son was harmed in some specific way, but if you gather your son's medical records an attorney can give you a more detailed assessment.