I think passengers on Community Transit and on Metro are not allowed to take so much baggage or packages on board with them, and there's nowhere else to put the items. You can check the Sounder website and see what they say.
There ARE no other ideas besides what Ira500 said. Taxi, Sounder, Community Transit and Metro are all there are. Call Shuttle Express and see if they'll pick you up and transport you to SeaTac, and do the opposite when you return. Otherwise, it's a taxi, or a friend driving you.
BTW, for just a 12-day trip, you should be taking only one carry-on suitcase that you can keep with you all the time, so it doesn't go to Spain while you're going to Germany. 12 days? Yes, that's one suitcase. If the rest is clothes, you don't need them. First rule of traveling: pack; then cut everything by at least 50%, and add at least 100% of the money you plan to have available.
Don't forget to check the TSA website to make certain you comply completely with their current packing regulations, and your airline(s)'s website(s) to comply with the current European security regulations.
Here are great tips for travel packing in general:
http://budgettravel.about.com/cs/pow...erful_pack.htm
and packing for U.S. airport security:
http://seniorliving.about.com/od/tra...velpacking.htm