I stumbled on a 2011 paper on maintaining Korean heritage Language from the perspective of Korean parents.  There is little here that I don’t know already, but I see that both ethnic Korean and Chinese parents share the same struggle.

https://files.eric.ed.gov/fulltext/EJ986889.pdf

“Perhaps more importantly, none of the students felt that Korean HL schools had made a difference in their HL maintenance. Based on what both the parents and students stated, it is fair to say that parents could not do the job of policing HL with their children, since the children were increasingly resistant to speaking and learning Korean.

Korean HL schools were therefore an easy alternative that the parents could count on in spite of the fact that their children hated those schools. While the parents might have agreed that the Korean HL schools were not effective, to stop sending their children would have been an admission of failure in HL maintenance. For these parents, the HL schools were a solution to the dilemma they faced, and the burden of teaching and monitoring Korean was turned over to those institutions…….

This remark strongly suggests that the parents themselves gradually reduced the use of HL and switched to English, perhaps because they felt that they were in fact capable of speaking in English. This might be the key reason why the student participants’ younger siblings’ seldom spoke Korean. The interviews revealed that in the cases of Derek, Gene, and Nina’s younger siblings, the use of Korean ranged from dismal to none.

It can be argued that the student participants in this study maintained HL not because of their parents’ determination or choice, but because of a lack of English proficiency at the beginning of their immigrated life. Of interest in Nina’s statement above is that there was not a time when Korean was used 100% of the time at home. This may be the reason why HL parents chose to send their children to Sunday HL schools, since they might well have felt that they could not maintain the HL at home, definitely feeling that they needed outside help. For these reasons Korean HL schools remain as one of the most popular choices for HL parents. “