Earlier quoted context omitted.
Again, wildly naive. There is no "rule of law" that is so prescriptive. We basically have a loose confederation of laws, interpreted by courts, and exacted by humans. There is flexibility in various aspects, including sentencing, and things like that are (when they are) left to the discretion of the judge precisely because there is no formula otherwise. There is nothing about this that violates anyone's oath or duty,…
I'm fine with a broad range of judicial discretion. Human judgement is a necessary part of the judicial system. I am not fine with someone being sentenced and jailed for a crime they were not found guilty of, which is what you're describing. That's an abuse of power and a deprivation of due process.
I ask you again to just use your imagination; set aside this particular case and imagine a case where there is absolutely compelling grounds for thinking that the mother is a direct harm to her children, but no admissible evidence to establish that in a legal context. So given the legal "room" to hand down a harsher-than-would-otherwise-be sentence for some separate offense, that doesn't strike me as totally inappropriate or out of line with our expectations about what judges should do. This of course requires the legal establishment of the "room" for judges to do such things, but they have that to a large extent.