"My daughter is almost 4". You better hurry to file the appropriate petition with the appropriate court. Once the daughter is 4, you will lose all rights to her if you have not been determined or have not filed the right petition to be determined as the child's legal parent.
In WA, the potential parents lose the right to challenge the parentage of the child once the child is 4 or older.
On another hand, the child never loses the child's right to an accurate determination of the child's parentage, even when the child is an adult, unless the child is represented by an attorney in a prior proceeding to determine the child's parentage. So, if the state attempts to collect child support after the child has turned 4, the court can still order genetic testing.
If you file the appropriate petition with the court, the court will order the mother to take a genetic test.
In WA, child support and time spend with a child are not linked together.
Again, you must act before the child is 4. You should review the specific facts with your attorney to find out your legal options.
File a petition to establish paternity in the county where the child last resided for six months. Do it quickly. File a motion for temporary orders asking for DNA testing and for a parenting plan allowing you time with your child. Child support will also probably be set by the court, but you said you are OK with that since a parent should financially support their chld. Do hurry, before your child is four years old.
It would be far far better for you to meet with a lawyer and get specific advice for your case and, if at all financially possible, for you to have a lawyer represent you. Get that case filed fast though.
If there has been no court order on paternity, you were never married, and no affidavit of paternity was filed, you can probably file a paternity case even after the 4 year mark. It’s always best to consult with a good family law attorney to discuss the details before you act. See my AVVO Legal Guides on paternity for more information about the legal issues raised by your inquiry. Click on my photo. On my AVVO home page click on "View Contributions" or scroll down further and click on "Legal Guides." Scroll down the list of my 29 Legal Guides and select the topics relevant to your question. If you like my answer and Legal Guides, please make sure you mark them as “helpful.”
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DSHS won't help you because it really isn't their function to sort out these things. While Prosecutor's Office is responsible for support enforcement, it isn't their job to disestablish paternity for the legal father in favor of the biological father. I am not sure what this in-home DNA test you used but it sounds like you are pretty sure the child is your biological child. I agree with everyone here. You have to file a petition. Speak to a family law attorney. If you can't really afford an attorney, try speaking to a family court facilitator at the local superior court house. It is usually around $25 to see them and they can at least get you all the document packet to fill out for your case. They can't give you legal advise but I guess that's somewhere you can start if you are going to go prose. Goodluck.