Opening a case does not equate to temporary removal of children. I work as a mentor with a few women who have open cases, but have not had "enough" to have their kids removed.
IMO, DHS would not take the kids away as a leverage technique. They have to maintain the dignity of their office as well. LE could indicate this as a strategy though, you are correct there.
IME (as a foster child/foster parent/child advocate/mentor) they are going to have to see evidence of more than just getting drunk to remove their kids. Emergency removal (most common form of removal, where removal precedes a hearing) requires justifiable indication of "imminent danger". Yes, Lisa went missing- but there is nothing public to indicate the other children are in imminent danger. Getting drunk in your home with kids is not illegal. They will need reason to believe that (sober or drunk) an action she made directly caused harm to come to Lisa, or could cause harm to her boys. Being drunk isn't enough. I do believe it will have to be more than not locking the door.
I know these statements makes me unpopular, but we don't have enough homes to provide perfect homes to all. Especially in this region with the massive meth problem, we are forced to concentrate on situations far more dire than getting drunk with your kids at home. JMO.
I think most people are very shocked at the extreme cases DHS works with.