You might try checking with the Pierce County Auditor/Recorder’s office to see if there is any written and recorded easement regarding the driveway. Any written easement language will be the first step in determining what governs the maintenance or exclusivity of any easement. Some records can be found online, see link below. You may also have these records in your title report from when you purchased.
If there is nothing in writing regarding maintenance or exclusive use of the easement, then it may be an easement by prescription. An easement by prescription is generally created by use over the passage of time (10 years). Whether or not this applies in your situation or whether there are additional factors you should consider discussing with a local real estate attorney.