(Kari) Hanayome no Yangotonaki Jijou

Ferdia is a workaholic orphan living in a church orphanage, helping take care of the younger children. One day, the King asks her to take a job substituting for his sickly younger sister. No problem—it's not her first time doing it, and the pay's gonna be great. But this time, her job is to wed a prince from an enemy country... And make him divorce her ASAP!

(Source: J-Novel Club Forums)