It's hard to respond helpfully with so little to go on.
Still, I'll dive in...
If a freshly painted house is already showing peeling and chalking, it's almost guaranteed it's due to inadequate/improper prep. All bubbling, peeling, wrinkling and alligatored paint should have been scraped and sanded and primed. Chalking occurs over time due to weathering, so if you've already got chalking, and you're sure the SW Emerald was used, it's hard to imagine the power washing was done competently.
Don't know what you mean by wood damage, nor the extent of the paint on shingles, so can't suggest anything there.
So....how to handle with contractor? First, look at your contract. What prep steps are listed? If little to none, your position is vastly weakened. However, there is a basic level of implied standard. Proper prep is one of them, as it's common knowledge that paint will not adhere to a dirty, peeling or otherwise failing surface. Every paint mfgr includes prep instruction right on the can.
Also, what representations do you have (in writing, email, text or on the contractor's marketing materials and website) as to guarantees, warranty and satisfaction? Take pictures. Lots. Head to your Sherwin Williams store and talk with one of the knowledgeable associates. They'll be able to diagnose and advise from a position of expertise with their product.
Hopefully, your contractor is a stand-up guy and will work with you to do what's necessary to get this right. Did you pay this contractor more than a minimal down payment, with balance due on accepted completion? Good! If you paid up-front, ouch. Your leverage in getting this remedied depends upon 1)the contractor's integrity and professionalism, and 2)a sizeable retained balance payment. If you did pay in full, and paid by credit card, you can try filing a dispute. Also, if you found your painter through a service like Home Advisor, Thumbtack, Angie's List, etc., you can try enlisting their help.
Without more specifics about your particular situation, it's hard to say just what a good remedy would be. But since most paint failure comes as a result of inadequate prep, I'd wager that the only real solution is a complete do-over.