Honestly, I think the CP takes the kids to counselors seriously hoping that they will say that they have problems because of NCP. Of course, that would never happen because the things that CP dreams up are not true things and the kids verify that. Thankfully most of the counselors have not been so screwed up that they will blatantly lie about what's up with the kids. However, they also don't tell NCP what is up with the kids either though. (won't actually speak against CP or anything)
So here's what I think happens--along about the time the counselor wakes up and starts realizing that the reason the kids have the emotional struggles that they have is a direct result of the CP and her parenting--she stops taking them to said counselor.
CP just tries to use the counseling as a threat with NCP. Then in about 2 months or so--when things settle down and the counselor sees CP's patterns---they suddenly stop going to the counselor. Go figure...
That's about the long & the short of it on this end.