Contempt is a quasi-criminal proceeding, but see RCW 26.09.160 requiring proof by a preponderance of the evidence, not clear and convincing evidence. Also, review Marriage of James, 79 Wn. App. 436, 442, 903 P.2d 470 (1995).
If you are not represented by an attorney, it can be tricky to prosecute this by yourself. You must obtain a show cause order, personally serve him, and establish that he willfully violated a lawful court order with which he had knowledge of and the ability to comply with. The court must make a finding that he acted in bad faith.
The usual defense is "I couldn't afford to pay for the evaluation" and that may be a valid defense to contempt. RCW 26.18.050(4). He may have other "excuses". The court may not believe his explanation, but he will probably have one. That might prevent the court from finding him in contempt and leave the problem unsolved.
What do you really want? You want to protect your kids. While contempt may be appropriate, I recommend you also consider filing a motion for an order that restricts or limits the father's contact with the children until he complies. You could join that motion with a contempt action if you really want to pursue contempt.
A motion is easier than a contempt action and still gets to the root of the problem.
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