Do any of you have a drivers license? It might be cheaper to rent a car for a day than to pay for a car service which would probably be considerable. I know my boss takes a town car from his home in Kirkland to SeaTac and it costs around $70 one way, and I would imagine it would cost at least that if not more from West Seattle to Woodinville each way.
Check out Uber – download the app on your smartphone and use it for on-demand car service. You might want to check the rates from WS to Woodinville first (the app allows you to get a fare quote). There are some options at different price points: UberX is lowest cost and the cars are smaller, like a Prius. Uber Black Car is town-car service, and UberXL is an SUV with room for 6.