Transit in Korea without a visa

From Timatic, the immigration database used by airlines, South Korea's transit visa exception policy (click through to "For details, click here") is rather complicated:

Visa Exemptions:

• Nationals of any country with a visa issued by Australia,

  Austria, Belgium, Canada, Cyprus, Czech Rep., Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland (Rep.), Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Netherlands, New Zealand, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, USA or United Kingdom if in transit through Korea (Rep.) must: -hold confirmed onward tickets on flights departing within

  30 days; when -arriving from the country that issued the visa and departing to a third country. (YVR-ICN-DEL); or

  -arriving from a third country and departing to the country

  that issued the visa (e.g. DEL-ICN-YVR); or -arriving from a third country after having transited that country for a maximum stay of 3 days, departing to the

  country that issued the visa (e.g. DEL-SGN-ICN-YVR); or -arriving from a third country, traveling to another country and staying there for a maximum stay of 3 days, then departing to the country that issued the visa (e.g.

  DEL-ICN-SGN-YVR).

  • This does not apply to nationals of Afghanistan, Cuba,

  Ghana, Iran, Iraq, Korea (Dem. People's Rep.), Kosovo (Rep.), Macedonia (FYROM), Nigeria, Sudan and Syria.

  • This does not apply to passengers with a document issued by the Palestinian Territory

As I understand this, you would not qualify and would need a visa. You are not transiting South Korea at all, but are visiting, going back and forth to China before going to the US. You would either need to receive a Korean visa or modify your itinerary to comply with these requirements.