When I put my children in a bilingual French-German program, I went to the meeting.
They announced that if the child already spoke another language, that this would NOT be a problem. I was happy to hear this because I use English and only English with mine. BUT they added, the child must be "well established" in the second language. They explained that they had many children who had to drop out of the program. They explained that in a child's mind, if they had not clearly separated the first two languages, the third one was difficult to master.
I saw several children leave for this reason. One mother was born here in France and although she grew up speaking Arabic to her family, she found it tough to keep to Arabic with her own son. His dad, directly from an Arabic speaking country, was determined he stay. It was a big stress because the poor little guy just couldn't grasp the German. When they finally did have to take him out, it was even further complicated with the fact he had to change schools entirely and leave his friends (including my son).
Another child, also with an English native speaking parent, it turns out that the family spoke more English at home than French and his French wasn't well established so that caused problems with the German. They were a "home vs. community" language as opposed to our OPOL situation (my kids are stronger in French than English).
If you child is not speaking Korean, she'll never learn to speak it. You do NOT need to "force" her to speak it but if you want her to learn it, you need to really encourage the Korean. I was able to get my son to use English and only English with me simply by being quicker in English, getting him what he wanted in English while in French, I "forgot", was slow or asked him to repeat.
Repeating everything really helped. No, not necessarily in English. I just made him repeat all French requests. He learned quickly that anything in French had to be said twice while if he used English, he got it right away and only had to say it once.
Don't be afraid to have standards and goals for your child. It's just like music, going to church or keeping their rooms clean. Some parents who are really strict with religion or homework get all sticky when it comes to speaking a foreign language. It's the same thing. If having your child speak Korean is important to you, don't be afraid to play your parent role!
It's so lovely to go home to the U.S. and have my kids just jump into my parents' arms as if they never stepped foot outside the States. Once we got the ball rolling, it was much, much easier than I thought. Even though my husband can't speak English and I lived and worked in France (speaking French) long before they were born, once I got used to speaking English to them, it was easy.
What's really satisfying is when I hear them switching between English, French and German with ease. We had a German exchange student as part of his schooling and my son was translating for me... As counter-logical as it sounds, being consistent with English really helped them learn German!