Unless the left out child is a minor, in WA, the child has no legal right to a share of the parent's estate against the wishes of the parent. In WA, a parent following statutory procedures can leave an adult child with nothing from the parent's estate. (One of the procedure would be to name the child specifically.)
The child can have an attorney reviews the specific facts to see whether the mother's will valid. If the will is not valid, the child would get a share under the intestate statute.
In the United States, people are pretty much guaranteed their day in court. The child cannot contest the Will because they have been excluded. But he/she may be able to contest it on grounds that 1) it was not properly executed; 2) the testator lacked mental capacity when the Will was executed; or 2) there was undue influence exerted which should nullify the Will.
The burden of proof would be against the contestant, and it can be a steep and expensive case, but if the child was determined to take it to court, there is not much that can be done to stop him/her. If there is no probable cause to find any valid reason to contest, there is a possibility that the court could impose sanctions on the plaintiff. I cannot recall a case when this was done that I worked on. MANY times, in cases such as this, the contesting child is offered a "nuisance settlement," in order to avoid the costs and delays of court.
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I do not practice in Washington and am not familiar with your laws, but in some states if the third child was born after the Will was executed, they may have a claim. Your fact summary is not specific regarding timing. Otherwise I would agree with the advice that has been given. You need to see a probate attorney.
I agree that a consultation with an experienced probate attorney is appropriate. I have three other comments to add to what has been said.
The gentleman from out of state mentioned that most states have statutes that could allow a child born after the execution of the will to take the share he or she would have received had there not been a will. In Washington, that is the omitted child statute--RCW 11.12.091. Those may not be your facts here, but I throw it out anyway.
Also, I would be surprised if this was the case, but if the excluded child is a minor and is not survived by his or her other parent, there is a statute in Washington that could award the child what is called a "family allowance.". RCW 11.54.010.
Nonetheless, contacting an attorney who will give you a frank and practical evaluation of the matter is critical. Court cases of this kind--especially if the case involves actually contesting the will--can be extremely expensive, a courts do in fact hold contestant liable for fees if the case lacks merit. Do rely on being paid in settlement to just "go away."