How should I respond to the other party in my parenting plan case, when he just threatens to "tell the court" for everything ?

Hearings in Superior court are by affidavit, meaning he has to execute a declaration in support of his motion, there is no live testimony. In Snohomish county, he must serve the motion on you 12 days before the hearing. He has to serve that declaration on you and you have the ability to respond with your own declaration 5 court days before the hearing. . That is how the process works. If he does file a motion, it would be wise to hire an attorney to assist you.

"Letters" to the court will have no effect; the court will not read them so you should try to ignore his threats. If you have a court-ordered parenting plan already, you should follow it carefully. You are under no obligation to offer him more time than the parenting plan affords. If you are in the process of getting a court-ordered parenting plan, then the parents may decide how to divide the child's time until a parenting plan is ordered. If there is a hearing scheduled or the father schedules one in the future, he will likely be able to testify, either orally or in writing, about what he did and what you did. But that doesn't mean that the court will believe everything he says or will consider it persuasive to the motion. Keep documented evidence, if you can, of your side of the story so that you have proof to show the judge if that ever becomes necessary. It sounds like a consult with an attorney or a more long term relationship with one would be helpful for you.

Ignore him and proceed with obeying the court orders in place. If he wants more time with the child he has to ask for it and show a reason. Until then don't worry about it. My own experience is that courts do not read letter sent to them from disgruntled parents. If he has a complain his option is to file a motion to have you held in contempt or to live with the issue, not to write to the court.