Trump sorgte für Empörung mit der Drohung, Soldaten einzusetzen.
Trump sorgte mit der Drohung, Soldaten einzusetzen, für Empörung.
Trump sorgte mit der Drohung für Empörung, Soldaten einzusetzen.
These three sentences are almost equivalent in meaning, consisting of three pieces of information:
(1) Trump
(2) caused outrage
(3) by the threat
(3a) to use soldiers
All are pretty much exchangeable, without even difference in meaning or connotation. German allows a lot of orders, and with non-obligatory phrases, most combinations work naturally.
Excourse: information packaging
What makes the examples different in conversation, though, is what part of the conveyed information is considered "background", and what part the speaker tries to convey as new.
There are some tendencies how that works:
- Known things come at the beginning
- "New" or "emphasized" things come at the end
- "Long" things, like additional information, come at the end.
The latter two points can conflict, as they do here. Additionally, the complexity in which the hearer can process them is different, and this is complicated by German separable verb constructions. Note, though, that these are not grammar rules: they are tendencies that speakers and writers will mostly follow to make utterances sound natural.
I have ordered the above sentences in terms of increasing complexity. Let me illustrate this by a hypothetical monologue in the hearer's mind:
Trump
OK, we know that it's about him.
Trump sorgte
He caused -- what?
Trump sorgte für Empörung
Whoah, he caused outrage! That's a complete sencente, are we
finished?
Trump sorgte für Empörung mit der Drohung
Ah, by the threat. But which specific threat do you mean?
Trump sorgte für Empörung mit der Drohung, Soldaten einsetzen
To use soldiers! Now I get it.
You see that at two points, the current processing is incomplete, and the hearer has to wait and keep in mind the current piece until it is resolved in the next piece. Compare that to what happens in the last example:
Trump
OK, we know that it's about him.
Trump sorgte
He caused -- what?
Trump sorgte mit der Drohung
Hä? Now what did he cause, with which threat?
Trump sorgte mit der Drohung für Empörung
Ah, he caused outrage by some threat. But still, which threat?
Trump sorgte für Empörung mit der Drohung, Soldaten einsetzen
To use solders! Why didn't you say that sooner.
What makes this more difficult is the two levels of missing information in Trump sorgte mit der Drohung, and the longer time that everything is needed to be kept.
The actual example
Back to our specific example:
So sorgte Trump nach dem Tod des Afroamerikaners George Floyd bei
einem brutalen Polizeieinsatz Ende Mai mit der Drohung für Empörung,
Berufssoldaten im Inland gegen gewalttätige Demonstranten einzusetzen.
So, as mentioned, that we are talking about Trump is already known and thus background. Then we set a more specific context: the death of Floyd at a specific time and place. At that point, we want to do two things: finishing the sorgte ... construction, and adding the required information in the object: what he caused.
The order in which those phrases are put is now almost indifferent. Für Empörung mit der Drohung I would slightly prefer, because it finishes the sorgte phrase earlier, emphasizes the additional information of the means, and puts the latter closer to it's subphrase.
However, in this case, the other variant sounds just as natural, perhaps with the slight difference of making the fact that Trump caused outrage more topicalized than the fact that he did it by a threat (we know that he threatens a lot, so that can even considered as "more background" already).
Finally, the long phrase "Berufssoldaten ... einzusetzen", specifying the threat, clearly belongs naturally to the end, because it is so long. We could equally say
So sorgte Trump nach dem Tod des Afroamerikaners George Floyd bei
einem brutalen Polizeieinsatz Ende Mai mit der Drohung, Berufssoldaten
im Inland gegen gewalttätige Demonstranten einzusetzen, für Empörung.
But then we'd have to wait way too long for the sorgte phrase to finish, making processing much harder. (This latter phenomenon, by the way, is what makes difficult German texts, e.g. from philosophers, so hard to follow.)