Can I apply for an H1 visa with a non-US based company?

the sponsor must be an US company/employer in order to petition H1b. you may be qualified for L1 visa. it applies to intracompany transferees who, within the three preceding years, have been employed abroad continuously for one year, and who will be employed by a branch, parent, affiliate, or subsidiary of that same employer in the U.S. in a managerial, executive, or specialized knowledge capacity.
L1 visa is similar to H1 visa. good luck.
http://travel.state.gov/visa/temp/types/types_1271.html
http://en.wikipedia.org/wiki/L-1_visa

A tourist visa would allow you to stay in the US for 90 days so figure out when best to spend that time. You can sit in a court room to offer moral support and not be in violation of that visa type. The fact that you're living in the UK and likely have established a life there should be helpful in your getting this visa you need.

I would think you would have to apply for a work visa in Spain, but your company's HR department should tell you.