If a visitation parenting plan is in place, is it illegal for the mother to break the plan without letting the child see his

Although I do not practice in your state, child support and visitation are two completely separate issues to most courts.

if you have a parenting plan and the mother isn't following it, you need to bring a contempt action to enforce it.

If the parenting plan is not being followed, then the father needs to bring a motion for contempt. Whether or not the father is paying support, the mother is still required to follow the parenting plan. Obviously, if the father is not paying support then the mother could file a motion for contempt for him not paying support. But as mentioned above, the requirement to pay support is completely separate from the requirement that the parents follow the parenting plan.

Below is the link to the WA state court forms for contempt. Contact the clerk's office or your courthouse facilitator to make sure you get the motion on the docket correctly. Note that in WA if a parent is found in contempt for not following the residential portions of a parenting plan two times in a three year period, that's ground to change custody. The father should not let the mother get into the habit of dictating when the parenting plan is followed.

I agree that contempt is the common remedy) but there are many defenses available). It is possible that her conduct qualifies as a crime, (See below). It would be rare for the police to investigate a common parenting plan dispute over whether the court order is being followed or not, and rarer still for that investigation to lead to a prosecution, but you should be aware of the statute. You should also confer with an attorney before trying to get the other party thrown in jail. Complaining that she is a criminal and should be arrested for custodial interference could make you look like a jerk and could backfire. This is particularly a concern if the mother alleges domestic violence.

RCW 9A.40.070
Custodial interference in the second degree.

(1) A relative of a person is guilty of custodial interference in the second degree if, with the intent to deny access to such person by a parent, guardian, institution, agency, or other person having a lawful right to physical custody of such person, the relative takes, entices, retains, detains, or conceals the person from a parent, guardian, institution, agency, or other person having a lawful right to physical custody of such person. This subsection shall not apply to a parent's noncompliance with a court-ordered parenting plan.

(2) A parent of a child is guilty of custodial interference in the second degree if: (a) The parent takes, entices, retains, detains, or conceals the child, with the intent to deny access, from the other parent having the lawful right to time with the child pursuant to a court-ordered parenting plan; or (b) the parent has not complied with the residential provisions of a court-ordered parenting plan after a finding of contempt under RCW 26.09.160(3); or (c) if the court finds that the parent has engaged in a pattern of willful violations of the court-ordered residential provisions.

(3) Nothing in subsection (2)(b) of this section prohibits conviction of custodial interference in the second degree under subsection (2)(a) or (c) of this section in absence of findings of contempt.

(4)(a) The first conviction of custodial interference in the second degree is a gross misdemeanor.

(b) The second or subsequent conviction of custodial interference in the second degree is a class C felony.