Unfortunately, there is one judicial officer in Lewis County who often does not seem to be helpful, and you might consider asking for review of this action by the presiding district court judge in Lewis County or a full-blown appeal to the Lewis County Superior Court if the commissioner ruled on your case. An appeal will cost you more than $200 but there are several reasons why you should be allowed to have a hearing on the merits in district court.
One thing you can do to deal with the Lewis County case without having to file an appeal is ask for review again in the District Court. You can find out from the clerk who ruled on your case, and as the person who ruled might be a commissioner, if that's the case you can write a letter to the presiding judge. If the person who ruled is a judge, I'm afraid that decision is probably only reviewable as an appeal to the Superior Court. There are time limits, so you should act expeditiously.
Commissioners are generally appointed by the presiding judge, but they often do not set court policy. It would be a poor policy if the Lewis County District Court did not allow a defendant in a civil traffic infraction case to have a continuance so that you can appear for a criminal case hearing in Snohomish County. And you are absolutely allowed a 'trial' for an infraction case; however, we generally call these 'trials' contested hearings. You are not entitled to a jury trial.
Finally, a seat belt ticket does not affect insurance premiums for regular drivers licensed in Washington; however, speeding tickets do affect premiums. Admitting to speeding does not help your premiums, but the safety belt violation does not actually hurt your premiums if you are a licensed WA driver applying for insurance in WA.
Don't feel like you're being screwed around by the courts. They are simply acting like this with everyone. If you didn't do something, you should have fought it in court and asked for a trial if you couldn't be at both at the same time. They would have adjourned it for trial and you could have come back and tried the case.
Or you could have consulted with an attorney to see how to handle it. However, since you did neither, this is the result they gave you. I'm sorry. Sometimes we all learn the hard way. This seems to have been your day.