So, Beeke is advocating refusing to feed your children if they refuse to participate in family worship. He has apparently not repudiated this. He said this during a conference in 2012 on the subject:

“So the next day you have family worship or that same night and there you see one of your children not singing, you pull him aside afterward and say ‘son, you will participate in this family worship’, and if he rebels and says, ‘Dad, I won’t do it’, you say, ‘son, no singing, no food.’ He will sing.”
http://www.sermonaudio.com/sermoninfo.asp?SID=82121557151

I think the problem is a problem of fear. We are afraid of calling out the abusers because we fear men more than God. God says the light exposes the deeds of darkness, but we have a better plan. We display grace through restoring the wolf and we show strong church discipline by beating the sheep. The sheep are powerless and the wolves have teeth. I will admit that I continue to live in fear of being bitten. I wonder if you’ll ever get to that. Abused sheep are messy, messy people. They’re bitter, they’re angry and they act out in very visible ways that church leaders think need to be disciplined, and the cycle continues.