meaning

expressions-françaises :

Le dictionnaire des expressions et locutions définit l’expression française c’est dans l’ordre des choses comme un événement normal, inévitable et prévisible.

wordreference :

that’s the way it goes, that’s the order of things, nothing to be done about it

Particular sentence

Sachez que dans l’ordre des choses, il nous est bien plus précieux que toi.

In your particular sentence, the verb savoir indicates the speaker is reminding the context, the natural, bounded to happen, order of things. In this context, "il" is more valuable than the listener.

You are right, in the first sentence “l’ordre des choses” expresses a natural consequence. “Ordre” has temporal and causative implications. Wiktionary provides the following definition:

Ce qui arrive, ce qui se passe, sans qu’il soit possible de le discuter, de le refuser.

Quite surprisingly, in the second sentence it’s used with a much more literal meaning. If all things were ranked according to how precious they are to us, he would come before you (by far). “Ordre” is to be understood as a comparison order, but using “ordre des choses” for a universal, absolute scale of importance in this way sounds very unusual¹ and quite literary.

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^{1. Apparently it was chosen for lack of a better translation that fits the format of subtitles.}