Yes, I believe if they are from the same incident, presumably under the same case number and the finding of guilt was at the same time, I believe you can move to vacate both. The statute allows for the vacation specifically of more than one dv charge if they are from the same incident. I see no reason why you would not be able to do the same in your situation. I'd be interested to see other opinions.
3 years after completing all of the sentencing obligations including paying off your fines, fees, restitution, etc. you can move the court to vacate.
My belief is that only one of those convictions can be vacated. To really begin the process, one must wait until 3 years have passed from the time the case is closed, and there are a list of requirements that must be fulfilled before the court would grant such a request. Consultation with an attorney would be wise on a case like this.
Some misdemeanors may be vacated from your record if you satisfy the WA statute (find it here: http://apps.leg.wa.gov/rcw/default.aspx?cite=9.96.060 ). FYI, vacated means the court will nullify the plea of guilty, allow the defendant to enter a plea of not guilty and then dismiss the conviction. At that point, the person may say for all purposes that they have never been convicted, including on employment applications.
Generally, the statute allows a misdemeanor to be vacated if:
(1) The applicant has no pending or new criminal charges, has never had a conviction vacated before, and does not have a current restraining, protection or no-contact order against them.
(2) The offense was not a violent offense (4th degree assault is not considered "violent" here), D.U.I., or sex offense and three or more years have passed since the person completed the terms of the original conditions of the sentence, including any financial obligations.
I believe it is an arguable position that both misdemeanors may be vacated-- if they have the same case number.
RCW 9.96.060 provides that: "An applicant may NOT have the record of conviction for a misdemeanor or gross misdemeanor offense vacated if: ... ...(g) The offender has been convicted of a NEW crime in this state, another state, or federal court since the date of conviction; [or] (h) The applicant has ever had the record of ANOTHER conviction vacated." (emphasis mine).
If the two misdemeanors are two separate counts with the same cause number, each conviction is neither a NEW crime, nor ANOTHER conviction-- thus allowing both counts to be vacated. I am not sure if that argument would work in practice, however.
Sorry for the technical answer. I too, would like to hear from other attorneys on this.
Anyway, based on your description alone, we can't be sure of your eligibility under this statute. However, If you are eligible, you can hire an attorney as soon as you would like to begin drafting the motions to vacate your conviction, and schedule the hearings.