I can understand why what looks on the face of it like a short(ish) sentence upsets some people, but I really don't like knee jerk reactions to what are usually very carefully considered sentencing decisions by professional judges and one here made in the context of an unusual and very distressing case.
The prosecution accepted a plea to culpable homicide (equivalent of manslaughter) rather than murder, on the basis of diminished responsibility. That can't happen unless the case has been looked at at the highest level of the prosecution service in Scotland. The plea to culpable homicide won't have been accepted without a great deal of thought going into it. The sentence is an extended sentence, which allows for a further four and half years of supervision and potential recall to prison. The judge stated that his starting point for the custodial sentence was 8 years. A one-third discount is standard for an early plea of guilty.
Incidentally in Scotland if you are sentenced to more than 4 years you are not guaranteed release halfway through your sentence. It is possible you may be released at that point if the Parole Board approve. Otherwise you will serve 2/3 of your sentence. Situation is different for life prisoners, who have to serve the custodial minimum part of their sentence before being considered by the Parole Board.
Ultimately if the prosecution think the sentence is unduly lenient they can appeal. Looking at the BBC report it seems like a very unusual case and one in which there were substantial MH problems short of insanity in the legal sense (which can lead to a not guilty by reason of insanity, but end up with an indefinite term in the State Hospital).
I am sure that if this woman were to have other children SS would be in there like a shot. Not vastly likely if she is 43 and likely to spend the next while in prison.