(I think the answer given by Ryan Reich is right on the money, but needs shoring up a bit, and so that is what I am attempting here.)
The short answer is that “Now then!” is a form of asserting / exercising artistic control.
The primal use of “now” is to announce that you are about to cross the (perceived) present moment in time.
The word “now” is therefore used, by extension, to introduce a new topic. A good example occurs in poem II of Housman’s “A Shropshire Lad”. Here are the first two stanzas:
Loveliest of trees, the cherry now
Is hung with bloom along the bough,
And stands about the woodland ride
Wearing white for Eastertide.
Now, of my threescore years and ten,
Twenty will not come again,
And take from seventy springs a score,
It only leaves me fifty more.
The “Now” at the beginning of the second stanza clearly serves merely to change the topic. Although the topic is, in fact, the current age of the speaker, that is merely a coincidence. One could just as easily change to some other line of thought:
Now, of all the pleasantries experienced by me,
Near the top are those around this tree.
And if I live to be as old as the hills,
This scene will never dim its thrills.
Ok, pure doggerel, but I had to make the point.
Also note that the “new topic” introduced by “now” might be void. That is, the only thing of interest or relevance is the breaking off from the previous topic.
The word “then” is often used (as others have noted) to mean “therefore”, or “henceforth”, and that is how it is used here.
In the example of a father saying “Now then!” addressing the misbehavior of his children, the need is felt at the gut level to underscore the transition by allocating the transitional expression its own slice of time. By saying “Now” you signal that you have just crossed into a new moment of time, and by immediately following it with “then”, you are announcing that that moment is being closed off and we are going into a completely new moment, somewhat like using double-paned windows in regions where the winter is severe. Notice that a less emphatic way of announcing the transition (across just one moment) would be to say “Now, now.”
Because “now” and “then” differ only by which side of the perceived present moment of time they are referencing, and it is often immaterial which side it is (the material thing being only the acknowledgement of that present moment as a dividing point), they can sometimes be used interchangeably. For example, “now” is used to mean “henceforth” in the following passage from poem XIX (TO AN ATHELETE DYING YOUNG) of that same book by Housman:
Eyes the shady night has shut
Cannot see the record cut,
And silence sounds no worse than cheers
After earth has stopped the ears:
Now you will not swell the rout
Of lads that wore their honours out,
Runners whom renown outran
And the name died before the man.
Notice that the above “Now” could easily be replaced by “Then”.
Neither “now” nor “then” fully captures the sense of “henceforth”, but since “henceforth” is such a cumbersome / unpoetic word, one of either “now” or “then” is (with poetic license, of course) pressed into service to supply this meaning. The concept of “henceforth” is that of the set [x, ∞), where x is the present point in time. Bear in mind that the present point in time has the same semantic weight as the entirety of all the future points in time. (After all, today is the first day of the rest of your life.) The word “now” focuses on x, whereas “then” focuses on the set of points after x. Therefore, which of these two words you press into service to mean “henceforth” is really a toss-up.