Hi Alex,

I've been screwed over a few times by Timatic and airlines.

Lets summarise;
1. US Passport
2. In Spain on a student visa.
3. Left Spain to Gatwick to do a visa run. Left on a student visa, to return on a standard Schengen visa/entry.
4. Got denied return boarding at Gatwick by Easyjet.
5. Presented information that contradicted KLM/Timatic data to the Gate Agent and Supervisor still denied boarding.
6. Got stuck in a hotel, wondering what to do.

Please correct me if the facts are wrong.

1. Contact your bank/card issuer and get a charge back on the Easyjet tickets/payment.
2. Contact Easyjet with a simplified version of events and explain how you are out of pocket.
Simplify and itemise the costs. Don't try for nonsense like they have to pay you because you are stressed, keep it to straight monetary costs.
3. Phone another airline and ask them about getting on the plane to Spain. If they get it then buy a ticket. Go to Spain
4. Give up on her taking a picture of your passport, you aren't in the US and A asserting your rights.
5. Follow the advice given above by people about airlines and rights, the EU has some pretty tough laws.

Keep to the facts and keep them cohesive and well presented, your initial rant isn't very clear.